Introduction to Random Graphs

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

[1]  H. Jeffreys,et al.  Theory of probability , 1896 .

[2]  L. M. M.-T. Theory of Probability , 1929, Nature.

[3]  E. N.,et al.  The Calculus of Finite Differences , 1934, Nature.

[4]  Edward Szpilrajn-Marczewski Sur deux propriétés des classes d'ensembles , 1945 .

[5]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[6]  R. Sitgreaves,et al.  PROBABILITY DISTRIBUTIONS RELATED TO RANDOM TRANSFORMATIONS OF A FINITE SET , 1954 .

[7]  H. Piaggio Mathematical Analysis , 1955, Nature.

[8]  Leo Katz,et al.  Probability of Indecomposability of a Random Mapping Function , 1955 .

[9]  A. Leaf GRAPH THEORY AND PROBABILITY , 1957 .

[10]  E. Wigner On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[11]  T. E. Harris A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  C. Nash-Williams Edge-disjoint spanning trees of finite graphs , 1961 .

[13]  W. T. Tutte,et al.  A Census of Planar Triangulations , 1962, Canadian Journal of Mathematics.

[14]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[15]  W. T. Tutte A Census of Planar Maps , 1963, Canadian Journal of Mathematics.

[16]  P. Erdös On an extremal problem in graph theory , 1970 .

[17]  J. Edmonds Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics - Journal Canadien de Mathematiques.

[18]  L. A. Shepp,et al.  Ordered cycle lengths in a random permutation , 1966 .

[19]  G. V. Balakin On Random Matrices , 1967 .

[20]  M. Tapia,et al.  Generation of Concave Node-Weighted Trees , 1967, IEEE Transactions on Circuit Theory.

[21]  A. Rényi,et al.  On the height of trees , 1967, Journal of the Australian Mathematical Society.

[22]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[23]  V. E. Stepanov On the Distribution of the Number of Vertices in Strata of a Random Tree , 1969 .

[24]  M. Dwass The total progeny in a branching process and a related random walk , 1969, Journal of Applied Probability.

[25]  V. E. Stepanov Limit Distributions of Certain Characteristics of Random Mappings , 1969 .

[26]  N. S. Barnett,et al.  Private communication , 1969 .

[27]  Yu. V. Glebskii,et al.  Range and degree of realizability of formulas in the restricted predicate calculus , 1969 .

[28]  A. Meir,et al.  Cutting down random trees , 1970, Journal of the Australian Mathematical Society.

[29]  A. Meir,et al.  The distance between points in random trees , 1970 .

[30]  O. Viskov Some comments on branching processes , 1970 .

[31]  Anatol Rapoport,et al.  Distribution of nodes of a tree by degree , 1970 .

[32]  A. V. Boyd,et al.  Formal power series and the total progeny in a branching process , 1971 .

[33]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .

[34]  V. F. Kolchin A problem of the Allocation of Particles in Cells and Cycles of Random Permutations , 1971 .

[35]  Igor N. Kovalenko,et al.  Theory of random graphs , 1971 .

[36]  C. Stein A bound for the error in the normal approximation to the distribution of a sum of dependent random variables , 1972 .

[37]  G. I. Ivchenko On the Asymptotic Behavior of Degrees of Vertices in a Random Graph , 1973 .

[38]  J. Moon,et al.  Combinatorics: The distance between nodes in recursive trees , 1974 .

[39]  A. Meir,et al.  Cutting down recursive trees , 1974 .

[40]  Louis H. Y. Chen Poisson Approximation for Dependent Trials , 1975 .

[41]  L. Pósa,et al.  Hamiltonian circuits in random graphs , 1976, Discret. Math..

[42]  Ronald Fagin,et al.  Probabilities on finite models , 1976, Journal of Symbolic Logic.

[43]  B. Bollobás,et al.  Cliques in random graphs , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[44]  A. Vershik,et al.  Limit Measures Arising in the Asympyotic Theory of Symmetric Groups. I. , 1977 .

[45]  J. Kingman The population structure associated with the Ewens sampling formula. , 1977, Theoretical population biology.

[46]  V. F. Kolchin Branching processes, random trees, and a generalized scheme of arrangements of particles , 1977 .

[47]  Vasek Chvátal,et al.  Determining the Stability Number of a Graph , 1976, SIAM J. Comput..

[48]  J. Gastwirth A Probability Model of a Pyramid Scheme , 1977 .

[49]  I. Gertsbakh Epidemic process on a random graph: some preliminary results , 1977, Journal of Applied Probability.

[50]  Edward M. Wright,et al.  The number of connected sparsely edged graphs , 1977, J. Graph Theory.

[51]  Ira M. Gessel,et al.  Stirling Polynomials , 1978, J. Comb. Theory, Ser. A.

[52]  Edward A. Bender,et al.  The Asymptotic Number of Labeled Graphs with Given Degree Sequences , 1978, J. Comb. Theory A.

[53]  Edward M. Wright,et al.  The number of connected sparsely edged graphs. II. Smooth graphs and blocks , 1978, J. Graph Theory.

[54]  P. Erdös,et al.  Biased Positional Games , 1978 .

[55]  J. Moon,et al.  On the Altitude of Nodes in Random Trees , 1978, Canadian Journal of Mathematics.

[56]  Colin McDiarmid,et al.  Determining the Chromatic Number of a Graph , 1979, SIAM J. Comput..

[57]  J. Spencer,et al.  EVOLUTION OF THE n-CUBE , 1979 .

[58]  David W. Walkup,et al.  On the Expected Value of a Random Assignment Problem , 1979, SIAM J. Comput..

[59]  Paul Erdös,et al.  Random Graph Isomorphism , 1980, SIAM J. Comput..

[60]  Y. D. Burtin On a simple formula for random mappings and its applications , 1980, Journal of Applied Probability.

[61]  C. McDiarmid Clutter percolation and random graphs , 1980 .

[62]  David W. Walkup,et al.  Matchings in random regular bipartite digraphs , 1980, Discret. Math..

[63]  Edward M. Wright,et al.  The number of connected sparsely edged graphs. III. Asymptotic results , 1980, J. Graph Theory.

[64]  Silvio Micali,et al.  An O(v|v| c |E|) algoithm for finding maximum matching in general graphs , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[65]  Geoffrey Grimmett,et al.  Random labelled trees and their branching networks , 1980 .

[66]  Béla Bollobás,et al.  Hadwiger's Conjecture is True for Almost Every Graph , 1980, Eur. J. Comb..

[67]  N. Martin,et al.  Mathematical Theory of Entropy , 1981 .

[68]  Béla Bollobás,et al.  Degree sequences of random graphs , 1981, Discret. Math..

[69]  D. Falikman Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix , 1981 .

[70]  E. Upfal,et al.  On factors in random graphs , 1981 .

[71]  János Komlós,et al.  The eigenvalues of random symmetric matrices , 1981, Comb..

[72]  János Komlós,et al.  The longest path in a random graph , 1981, Comb..

[73]  F. Juhász On the spectrum of a random graph , 1981 .

[74]  Béla Bollobás,et al.  The Diameter of Random Graphs , 1981 .

[75]  Richard M. Karp,et al.  Maximum Matchings in Sparse Random Graphs , 1981, FOCS 1981.

[76]  Béla Bollobás Long paths in sparse random graphs , 1982, Comb..

[77]  C. C. Heyde,et al.  On the number of terminal vertices in certain random trees with an application to stemma construction in philology , 1982, Journal of Applied Probability.

[78]  B. Bollobás Distinguishing Vertices of Random Graphs , 1982 .

[79]  A. Barbour Poisson convergence and random graphs , 1982 .

[80]  Béla Bollobás,et al.  Vertices of given degree in a random graph , 1982, J. Graph Theory.

[81]  János Komlós,et al.  Largest random component of ak-cube , 1982, Comb..

[82]  Alan M. Frieze,et al.  On the connectivity of random m-orientable graphs and digraphs , 1982, Comb..

[83]  Michal Karonski,et al.  A review of random graphs , 1982, J. Graph Theory.

[84]  Miklós Simonovits,et al.  Supersaturated graphs and hypergraphs , 1983, Comb..

[85]  Jeanette P. Schmidt,et al.  A threshold for perfect matchings in random d-pure hypergraphs , 1983, Discret. Math..

[86]  Boris Pittel,et al.  On Distributions Related to Transitive Closures of Random Finite Mappings , 1983 .

[87]  M. Karonski,et al.  On the number of strictly balanced subgraphs of a random graph , 1983 .

[88]  Helmut Prodinger,et al.  On monotone functions of tree structures , 1983, Discret. Appl. Math..

[89]  Sven Berg Random contact processes, snowball sampling and factorial series distributions , 1983 .

[90]  Jerzy Jaworski On a random mapping (T, Pj ) , 1984 .

[91]  Zbigniew Palka On the number of vertices of given degree in a random graph , 1984, J. Graph Theory.

[92]  Frank Thomson Leighton,et al.  Graph Bisection Algorithms with Good Average Case Behavior , 1984, FOCS.

[93]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[94]  Colin McDiarmid,et al.  Topics in Chromatic Graph Theory: Colouring random graphs , 2015 .

[95]  Jeanette P. Schmidt,et al.  Component structure in the evolution of random hypergraphs , 1985, Comb..

[96]  Alan M. Frieze,et al.  On the value of a random minimum spanning tree problem , 1985, Discret. Appl. Math..

[97]  Alan M. Frieze,et al.  An algorithm for finding Hamilton cycles in random graphs , 1985, STOC '85.

[98]  J. Komlos,et al.  First Occurrence of Hamilton Cycles in Random Graphs , 1985 .

[99]  D. Aldous Exchangeability and related topics , 1985 .

[100]  E. Györi,et al.  Every graph is contained in a sparsest possible balanced graph , 1985 .

[101]  Alan M. Frieze Maximum matchings in a class of random graphs , 1986, J. Comb. Theory, Ser. B.

[102]  Martin E. Dyer,et al.  On linear programs with random costs , 1986, Math. Program..

[103]  Alan M. Frieze On large matchings and cycles in sparse random graphs , 1986, Discret. Math..

[104]  Andrzej Rucinski,et al.  Strongly balanced graphs and random graphs , 1986, J. Graph Theory.

[105]  Fan Chung Graham,et al.  Some intersection theorems for ordered sets and graphs , 1986, J. Comb. Theory, Ser. A.

[106]  Joel H. Spencer,et al.  Sharp concentration of the chromatic number on random graphsGn, p , 1987, Comb..

[107]  J. Szymanski On a Nonuniform Random Recursive Tree , 1987 .

[108]  Svante Janson,et al.  Poisson convergence and poisson processes with applications to random graphs , 1987 .

[109]  J. Michael Steele,et al.  On Frieze's χ(3) limit for lengths of minimal spanning trees , 1987, Discret. Appl. Math..

[110]  D. W. MATULA Expose-and-merge exploration and the chromatic number of a random graph , 1987, Comb..

[111]  Zbigniew Palka,et al.  Extreme degrees in random graphs , 1987, J. Graph Theory.

[112]  Saharon Shelah,et al.  Expected Computation Time for Hamiltonian Path Problem , 1987, SIAM J. Comput..

[113]  A. Rucinski,et al.  Poisson convergence and semi-induced properties of random graphs , 1987, Mathematical Proceedings of the Cambridge Philosophical Society.

[114]  Martin Dyer,et al.  On the Strength of Connectivity of Random Subgraphs of the n-Cube , 1987 .

[115]  B. Bollobás,et al.  An algorithm for finding hamilton paths and cycles in random graphs , 1987 .

[116]  R. Karp An Upper Bound on the Expected Cost of an Optimal Assignment , 1987 .

[117]  Jerzy Jaworski,et al.  On a Random Digraph , 1987 .

[118]  A. Frieze ON MATCHINGS AND HAMILTON CYCLES IN RANDOM GRAPHS , 1988 .

[119]  Benjamin Weiss,et al.  When are random graphs connected , 1988 .

[120]  Béla Bollobás,et al.  The chromatic number of random graphs , 1988, Comb..

[121]  J. Spencer,et al.  Zero-one laws for sparse random graphs , 1988 .

[122]  Svante Janson,et al.  Normal Convergence by Higher Semiinvariants with Applications to Sums of Dependent Random Variables and Random Graphs , 1988 .

[123]  Andrzej Ruciflski When are small subgraphs of a random graph normally distributed , 1988 .

[124]  Andrzej Rucinski,et al.  A central limit theorem for decomposable random variables with applications to random graphs , 1989, J. Comb. Theory B.

[125]  Endre Szemerédi,et al.  On the second eigenvalue of random regular graphs , 1989, STOC '89.

[126]  C. McDiarmid,et al.  On random minimum length spanning trees , 1989 .

[127]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

[128]  Andrew Thomason A simple linear expected time algorithm for finding a hamilton path , 1989, Discret. Math..

[129]  Alan M. Frieze,et al.  On the number of hamilton cycles in a random graph , 1989, J. Graph Theory.

[130]  Boris G. Pittel,et al.  On Tree Census and the Giant Component in Sparse Random Graphs , 1990, Random Struct. Algorithms.

[131]  R. Gray Entropy and Information Theory , 1990, Springer New York.

[132]  Alan Frieze,et al.  Edge disjoint spanning trees in random graphs , 1990 .

[133]  Tomasz Luczak On the Number of Sparse Connected Graphs , 1990, Random Struct. Algorithms.

[134]  Richard M. Karp,et al.  The Transitive Closure of a Random Digraph , 1990, Random Struct. Algorithms.

[135]  Alan M. Frieze,et al.  On the independence number of random graphs , 1990, Discret. Math..

[136]  Rajeev Motwani,et al.  Stable husbands , 1990, SODA '90.

[137]  Béla Bollobás Complete Matchings in Random Subgraphs on the Cube , 1990, Random Struct. Algorithms.

[138]  Svante Janson,et al.  Small Cliques in Random Graphs , 1990, Random Struct. Algorithms.

[139]  Svante Janson,et al.  Poisson Approximation for Large Deviations , 1990, Random Struct. Algorithms.

[140]  Svante Janson,et al.  A Functional Limit Theorem for Random Graphs with Applications to Subgraph Count Statistics , 1990, Random Struct. Algorithms.

[141]  Brendan D. McKay,et al.  Asymptotic enumeration by degree sequence of graphs with degreeso(n1/2) , 1991, Comb..

[142]  Alan M. Frieze,et al.  Spanning Maximal Planar Subgraphs of Random Graphs , 1991, Random Struct. Algorithms.

[143]  Tomasz Luczak,et al.  Cycles in a Random Graph Near the Critical Point , 1991, Random Struct. Algorithms.

[144]  Tomasz Luczak A note on the sharp concentration of the chromatic number of random graphs , 1991, Comb..

[145]  Tomasz Luczak,et al.  Size and connectivity of the k-core of a random graph , 1991, Discret. Math..

[146]  S. Janson,et al.  The asymptotic distributions of generalized U-statistics with applications to random graphs , 1991 .

[147]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[148]  David Aldous,et al.  Asymptotic Fringe Distributions for General Families of Random Trees , 1991 .

[149]  Colin McDiarmid Expected numbers at hitting times , 1991, J. Graph Theory.

[150]  Vasek Chvátal,et al.  Almost All Graphs with 1.44n Edges are 3-Colorable , 1991, Random Struct. Algorithms.

[151]  Tomasz Luczak The chromatic number of random graphs , 1991, Comb..

[152]  Andrzej Rucinski,et al.  Tree-Matchings in Graph Processes , 1991, SIAM J. Discret. Math..

[153]  Colin Cooper Pancyclic Hamilton cycles in random graphs , 1991, Discret. Math..

[154]  Edward A. Bender,et al.  The number of rooted maps on an orientable surface , 1991, J. Comb. Theory, Ser. B.

[155]  D. Aldous Asymptotics in the random assignment problem , 1992 .

[156]  Alan M. Frieze,et al.  On the independence and chromatic numbers of random regular graphs , 1992, J. Comb. Theory, Ser. B.

[157]  Colin Cooper On the Trickness of Sparse Random Graphs , 1992, Comb. Probab. Comput..

[158]  Colin Cooper 1-Pancyclic Hamilton Cycles in Random Graphs , 1992, Random Struct. Algorithms.

[159]  Mark Jerrum,et al.  Large Cliques Elude the Metropolis Process , 1992, Random Struct. Algorithms.

[160]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[161]  Philippe Flajolet,et al.  Varieties of Increasing Trees , 1992, CAAP.

[162]  Nicholas C. Wormald,et al.  Random Graph Processes with Degree Restrictions , 1992, Combinatorics, Probability and Computing.

[163]  R. Arratia,et al.  The Cycle Structure of Random Permutations , 1992 .

[164]  Nicholas C. Wormald,et al.  Almost All Cubic Graphs Are Hamiltonian , 1992, Random Struct. Algorithms.

[165]  B. Pittel On Likely Solutions of a Stable Marriage Problem , 1992 .

[166]  Andrzej Rucinski,et al.  Matching and covering the vertices of a random graph by copies of a given graph , 1992, Discret. Math..

[167]  Andrzej Rucinski,et al.  Ramsey properties of random graphs , 1992, J. Comb. Theory, Ser. B.

[168]  Hosam M. Mahmoud,et al.  Evolution of random search trees , 1991, Wiley-Interscience series in discrete mathematics and optimization.

[169]  Noga Alon,et al.  Choice Numbers of Graphs: a Probabilistic Approach , 1992, Combinatorics, Probability and Computing.

[170]  Yoshiharu Kohayakawa,et al.  The Evaluation of Random Subgraphs of the Cube , 1992, Random Struct. Algorithms.

[171]  Tomasz Luczak,et al.  Cycles in a Uniform Graph Process , 1992, Combinatorics, Probability and Computing.

[172]  Svante Janson Multicyclic Components in a Random Graph Process , 1993, Random Struct. Algorithms.

[173]  B. Pittel,et al.  The average performance of the greedy matching algorithm , 1993 .

[174]  Noga Alon,et al.  Threshold Functions for H-factors , 1993, Comb. Probab. Comput..

[175]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[176]  Jerzy Szymanski,et al.  On the Structure of Random Plane-oriented Recursive Trees and Their Branches , 1993, Random Struct. Algorithms.

[177]  Svante Janson,et al.  The Birth of the Giant Component , 1993, Random Struct. Algorithms.

[178]  N. Alon Restricted colorings of graphs , 1993 .

[179]  Alexander H. G. Rinnooy Kan,et al.  Average Case Analysis of a Heuristic for the Assignment Problem , 1994, Math. Oper. Res..

[180]  B. Pittel,et al.  The structure of a random graph at the point of the phase transition , 1994 .

[181]  Alan M. Frieze,et al.  Optimal construction of edge-disjoint paths in random graphs , 1994, SODA '94.

[182]  Alan M. Frieze,et al.  Multicolored Trees in Random Graphs , 1994, Random Struct. Algorithms.

[183]  Wen-Chin Chen,et al.  Heap-ordered Trees, 2-Partitions and Continued Fractions , 1994, Eur. J. Comb..

[184]  Jim Pitman,et al.  Brownian bridge asymptotics for random mappings , 1992, Advances in Applied Probability.

[185]  M. Talagrand Concentration of measure and isoperimetric inequalities in product spaces , 1994, math/9406212.

[186]  Svante Janson,et al.  The Numbers of Spanning Trees, Hamilton Cycles and Perfect Matchings in a Random Graph , 1994, Combinatorics, Probability and Computing.

[187]  Boris G. Pittel,et al.  Note on the Heights of Random Recursive Trees and Random m-ary Search Trees , 1994, Random Struct. Algorithms.

[188]  Alan M. Frieze,et al.  Hamilton Cycles in Random Regular Digraphs , 1994, Combinatorics, Probability and Computing.

[189]  Nicholas C. Wormald,et al.  Almost All Regular Graphs Are Hamiltonian , 1994, Random Struct. Algorithms.

[190]  Svante Janson,et al.  The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph , 1995, Random Struct. Algorithms.

[191]  Alan M. Frieze,et al.  On the Connectivity of Random k-th Nearest Neighbour Graphs , 1995, Combinatorics, Probability and Computing.

[192]  Yoshiharu Kohayakawa,et al.  Connectivity Properties of Random Subgraphs of the Cube , 1995, Random Struct. Algorithms.

[193]  E. M. Palmer,et al.  Hitting time fork edge-disjoint spanning trees in a random graph , 1995 .

[194]  Luc Devroye,et al.  The Strong Convergence of Maximal Degrees in Uniform Random Recursive Trees and Dags , 1995, Random Struct. Algorithms.

[195]  V. Rödl,et al.  Threshold functions for Ramsey properties , 1995 .

[196]  Alan M. Frieze,et al.  Multicoloured Hamilton cycles in random graphs; an anti-Ramsey threshold , 1995, Electron. J. Comb..

[197]  Yoshiharu Kohayakawa,et al.  Turán's Extremal Problem in Random Graphs: Forbidding Even Cycles , 1995, J. Comb. Theory, Ser. B.

[198]  Noga Alon,et al.  A Note on Network Reliability , 1995 .

[199]  Ludek Kucera,et al.  Expected Complexity of Graph Partitioning Problems , 1995, Discret. Appl. Math..

[200]  Svante Janson,et al.  Random Regular Graphs: Asymptotic Distributions and Contiguity , 1995, Combinatorics, Probability and Computing.

[201]  Peter Winkler,et al.  On the Size of a Random Maximal Graph , 1995, Random Struct. Algorithms.

[202]  Alan M. Frieze,et al.  Perfect Matchings in Random r-regular, s-uniform Hypergraphs , 1996, Combinatorics, Probability and Computing.

[203]  Alan M. Frieze,et al.  Generating and Counting Hamilton Cycles in Random Regular Graphs , 1996, J. Algorithms.

[204]  Y. Kohayakawa,et al.  Turán's extremal problem in random graphs: Forbidding odd cycles , 1996, Comb..

[205]  Joel H. Spencer,et al.  Sudden Emergence of a Giantk-Core in a Random Graph , 1996, J. Comb. Theory, Ser. B.

[206]  Erhard Godehardt,et al.  On the connectivity of a random interval graph , 1996, Random Struct. Algorithms.

[207]  G. Kalai,et al.  Every monotone graph property has a sharp threshold , 1996 .

[208]  Helmut Prodinger Depth and Path Length of Heap Ordered Trees , 1996, Int. J. Found. Comput. Sci..

[209]  Alan M. Frieze,et al.  An efficient algorithm for the vertex-disjoint paths problem in random graphs , 1996, SODA '96.

[210]  V. Sachkov Combinatorial Methods in Discrete Mathematics , 1996 .

[211]  David R. Karger,et al.  A new approach to the minimum cut problem , 1996, JACM.

[212]  Robert T. Smythe,et al.  Poisson approximations for functionals of random trees , 1996, Random Struct. Algorithms.

[213]  A universal bijection between Gessel-Stanley permutations and connection diagrams of corresponding ranks , 1996 .

[214]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[215]  Joel Spencer ENUMERATING GRAPHS AND BROWNIAN MOTION , 1997 .

[216]  T. Lu ON K4-FREE SUBGRAPHS OF RANDOM GRAPHS , 1997 .

[217]  Yoshiharu Kohayakawa,et al.  OnK4-free subgraphs of random graphs , 1997, Comb..

[218]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[219]  Hanna D. Robalewska,et al.  1-Factorizations of random regular graphs , 1997, Random Struct. Algorithms.

[220]  David A. Grable,et al.  On Random Greedy Triangle Packing , 1997, Electron. J. Comb..

[221]  Brendan D. McKay,et al.  The degree sequence of a random graph. I. The models , 1997, Random Struct. Algorithms.

[222]  David Aldous,et al.  Brownian excursions, critical random graphs and the multiplicative coalescent , 1997 .

[223]  J. Bourgain,et al.  Influences of Variables and Threshold Intervals under Group Symmetries , 1997 .

[224]  Noga Alon,et al.  The concentration of the chromatic number of random graphs , 1997, Comb..

[225]  Alan M. Frieze,et al.  Maximum matchings in sparse random graphs: Karp-Sipser revisited , 1998, Random Struct. Algorithms.

[226]  Bruce A. Reed,et al.  The Size of the Giant Component of a Random Graph with a Given Degree Sequence , 1998, Combinatorics, Probability and Computing.

[227]  G. Parisi A Conjecture on random bipartite matching , 1998, cond-mat/9801176.

[228]  Jerzy Jaworski Predecessors in a random mapping , 1998, Random Struct. Algorithms.

[229]  Noga Alon,et al.  Finding a large hidden clique in a random graph , 1998, SODA '98.

[230]  Tomasz Luczak Random trees and random graphs , 1998, Random Struct. Algorithms.

[231]  B. Sudakov,et al.  The chromatic numbers of random hypergraphs , 1998, Random Struct. Algorithms.

[232]  Yoshiharu Kohayakawa,et al.  An Extremal Problem For Random Graphs And The Number Of Graphs With Large Even-Girth , 1998, Comb..

[233]  Johan Jonasson On the Cover Time for Random Walks on Random Graphs , 1998, Comb. Probab. Comput..

[234]  Alan M. Frieze,et al.  Random Minimum Length Spanning Trees in Regular Graphs , 1998, Comb..

[235]  Jiang-Hua Lu,et al.  STRONG CONSISTENCY OF THE NUMBER OF VERTICES OF GIVEN DEGREES IN NONUNIFORM RANDOM RECURSIVE TREES , 1998 .

[236]  Jerzy Jaworski Epidemic processes on digraphs of random mappings , 1999 .

[237]  Svante Janson,et al.  One, Two and Three Times log n/n for Paths in a Complete Graph with Random Weights , 1999, Combinatorics, Probability and Computing.

[238]  N. Wormald,et al.  Models of the , 2010 .

[239]  N. Wormald The differential equation method for random graph processes and greedy algorithms , 1999 .

[240]  Boris G. Pittel,et al.  The random bipartite nearest neighbor graphs , 1999, Random Struct. Algorithms.

[241]  Gregory L. McColm,et al.  First order zero-one laws for random graphs on the circle , 1999, Random Struct. Algorithms.

[242]  Mathew D. Penrose,et al.  On k-connectivity for a geometric random graph , 1999, Random Struct. Algorithms.

[243]  Don Coppersmith,et al.  Constructive bounds and exact expectations for the random assignment problem , 1998, Random Struct. Algorithms.

[244]  Noga Alon,et al.  List Coloring of Random and Pseudo-Random Graphs , 1999, Comb..

[245]  D. Coppersmith,et al.  Constructive bounds and exact expectation for the random assignment problem , 1999 .

[246]  E. Friedgut,et al.  Sharp thresholds of graph properties, and the -sat problem , 1999 .

[247]  Bruce A. Reed,et al.  Colouring proximity graphs in the plane , 1999, Discret. Math..

[248]  Piyush Gupta,et al.  Critical Power for Asymptotic Connectivity in Wireless Networks , 1999 .

[249]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[250]  Eric Vigoda,et al.  Improved bounds for sampling colorings , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[251]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[252]  Edward R. Scheinerman,et al.  On Random Intersection Graphs: The Subgraph Problem , 1999, Combinatorics, Probability and Computing.

[253]  J. Pitman,et al.  Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions , 1999, math/9912170.

[254]  Alan M. Frieze,et al.  Optimal construction of edge-disjoint paths in random regular graphs , 2000, SODA '99.

[255]  Oliver Riordan,et al.  The Maximum Degree Of A Random Graph , 2000, Comb. Probab. Comput..

[256]  Random Lifts of Graphs III : Independence and Chromatic , 2000 .

[257]  Alan M. Frieze,et al.  Hamilton cycles in random graphs and directed graphs , 2000, Random Struct. Algorithms.

[258]  Oliver Riordan,et al.  Spanning Subgraphs of Random Graphs , 2000, Combinatorics, Probability and Computing.

[259]  Michael Krivelevich,et al.  Two‐coloring random hypergraphs , 2002, Random Struct. Algorithms.

[260]  James Allen Fill,et al.  Random intersection graphs when m= w (n): an equivalence theorem relating the evolution of the G ( n, m, p ) and G ( n,P /italic>) models , 2000 .

[261]  Michael Krivelevich The Choice Number Of Dense Random Graphs , 2000, Comb. Probab. Comput..

[262]  Noga Alon,et al.  UNIVERSALITY AND TOLERANCE (Extended Abstract) , 2000 .

[263]  N. Alon,et al.  On the concentration of eigenvalues of random symmetric matrices , 2000, math-ph/0009032.

[264]  Béla Bollobás,et al.  Constrained Graph Processes , 2000, Electron. J. Comb..

[265]  Tomasz Luczak,et al.  Biased Positional Games for Which Random Strategies are Nearly Optimal , 2000, Comb..

[266]  Alan M. Frieze,et al.  A Note on Random Minimum Length Spanning Trees , 2000, Electron. J. Comb..

[267]  Tomasz Luczak On triangle-free random graphs , 2000, Random Struct. Algorithms.

[268]  Jon M. Kleinberg,et al.  The small-world phenomenon: an algorithmic perspective , 2000, STOC '00.

[269]  Benny Sudakov,et al.  Random regular graphs of high degree , 2001, Random Struct. Algorithms.

[270]  Jim Pitman,et al.  Random mappings, forests, and subsets associated with Abel-Cayley-Hurwitz multinomial expansions , 2001 .

[271]  Alan M. Frieze,et al.  Avoiding a giant component , 2001, Random Struct. Algorithms.

[272]  Maria J. Serna,et al.  Approximating Layout Problems on Random Geometric Graphs , 2001, J. Algorithms.

[273]  J. Radhakrishnan Entropy and Counting ∗ , 2001 .

[274]  P. ERDbS ON THE STRENGTH OF CONNECTEDNESS OF A RANDOM GRAPH , 2001 .

[275]  Philippe Flajolet,et al.  Random maps, coalescing saddles, singularity analysis, and Airy phenomena , 2001, Random Struct. Algorithms.

[276]  Michael Krivelevich,et al.  Choosability in Random Hypergraphs , 2001, J. Comb. Theory, Ser. B.

[277]  J. Hopcroft,et al.  Are randomly grown graphs really random? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[278]  L. Moser,et al.  AN EXTREMAL PROBLEM IN GRAPH THEORY , 2001 .

[279]  J. Spencer The Strange Logic of Random Graphs , 2001 .

[280]  Jirí Matousek,et al.  Random lifts of graphs , 2001, SODA '01.

[281]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[282]  Nicholas C. Wormald,et al.  Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs , 2001, J. Comb. Theory, Ser. B.

[283]  Alan M. Frieze,et al.  Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity , 2002, Combinatorics, Probability and Computing.

[284]  T. F. Móri On random trees , 2002 .

[285]  Alan M. Frieze,et al.  Multi-Coloured Hamilton Cycles in Random Edge-Coloured Graphs , 2002, Combinatorics, Probability and Computing.

[286]  J. Dall,et al.  Random geometric graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[287]  Virgil D. Gligor,et al.  A key-management scheme for distributed sensor networks , 2002, CCS '02.

[288]  B. Söderberg General formalism for inhomogeneous random graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[289]  F. Chung,et al.  Eigenvalues of Random Power law Graphs , 2003 .

[290]  Nathan Linial,et al.  Random Graph Coverings I: General Theory and Graph Connectivity , 2002, Comb..

[291]  Piet Van Mieghem,et al.  On the covariance of the level sizes in random recursive trees , 2002, Random Struct. Algorithms.

[292]  J. H. Kima Sandwiching random graphs : universality between random graph models , 2002 .

[293]  Cristopher Moore,et al.  Almost all graphs with average degree 4 are 3-colorable , 2002, STOC '02.

[294]  Tomasz Łuczak,et al.  The phase transition in a random hypergraph , 2002 .

[295]  Edward A. Bender,et al.  The Number of Labeled 2-Connected Planar Graphs , 2002, Electron. J. Comb..

[297]  Christos H. Papadimitriou,et al.  On the Eigenvalue Power Law , 2002, RANDOM.

[298]  Zbigniew Palka,et al.  Remarks on a general model of a random digraph , 2002, Ars Comb..

[299]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[300]  F. Chung,et al.  The average distances in random graphs with given expected degrees , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[301]  Colin McDiarmid,et al.  Random channel assignment in the plane , 2003, Random Struct. Algorithms.

[302]  장윤희,et al.  Y. , 2003, Industrial and Labor Relations Terms.

[303]  Benny Sudakov,et al.  On the probability of independent sets in random graphs , 2003, Random Struct. Algorithms.

[304]  Ingo Schiermeyer,et al.  The Ramsey number r(C7, C7, C7) , 2003, Discuss. Math. Graph Theory.

[305]  Alan M. Frieze,et al.  On Randomly Generated Intersecting Hypergraphs , 2003, Electron. J. Comb..

[306]  Boris G. Pittel,et al.  Existence of a perfect matching in a random (1+e-1)--out bipartite graph , 2003, J. Comb. Theory, Ser. B.

[307]  Alan M. Frieze,et al.  Perfect matchings in random graphs with prescribed minimal degree , 2003, SODA '03.

[308]  Rick Durrett,et al.  Rigorous Result for the CHKNS Random Graph Model , 2003, DRW.

[309]  Svante Linusson,et al.  A proof of Parisi’s conjecture on the random assignment problem , 2003, math/0303214.

[310]  Deryk Osthus,et al.  On random planar graphs, the number of planar graphs and their triangulations , 2003, J. Comb. Theory, Ser. B.

[311]  Erhard Godehardt,et al.  Two Models of Random Intersection Graphs for Classification , 2003 .

[312]  Alan M. Frieze,et al.  A general model of web graphs , 2003, Random Struct. Algorithms.

[313]  Cristopher Moore,et al.  Almost all graphs with average degree 4 are 3-colorable , 2003, J. Comput. Syst. Sci..

[314]  Alan M. Frieze,et al.  High Degree Vertices and Eigenvalues in the Preferential Attachment Graph , 2005, Internet Math..

[315]  Assaf Naor,et al.  The two possible values of the chromatic number of a random graph , 2004, STOC '04.

[316]  A. RÉNY,et al.  ON THE EXISTENCE OF A FACTOR OF DEGREE ONE OF A CONNECTED RANDOM GRAPH , 2004 .

[317]  A. Frieze,et al.  The Size of the Largest Strongly Connected Component of a Random Digraph with a Given Degree Sequence , 2004, Combinatorics, Probability and Computing.

[318]  Béla Bollobás,et al.  The Diameter of a Scale-Free Random Graph , 2004, Comb..

[319]  Christos Faloutsos,et al.  R-MAT: A Recursive Model for Graph Mining , 2004, SDM.

[320]  S. Rai The Spectrum of a Random Geometric Graph is Concentrated , 2004, math/0408103.

[321]  Cristopher Moore,et al.  The Chromatic Number of Random Regular Graphs , 2004, APPROX-RANDOM.

[322]  Dudley Stark The vertex degree distribution of random intersection graphs , 2004, Random Struct. Algorithms.

[323]  . N.S.F.GrantsDmsandDms,et al.  Brownian Bridge Asymptotics for Random p-Mappings , 2004 .

[324]  Helmut Prodinger,et al.  On Some Parameters in Heap Ordered Trees , 2004, Comb. Probab. Comput..

[325]  Alan M. Frieze,et al.  A Geometric Preferential Attachment Model of Networks , 2004, WAW.

[326]  S. Janson,et al.  Upper tails for subgraph counts in random graphs , 2004 .

[327]  Luc Devroye,et al.  Branching processes in the analysis of the heights of trees , 1987, Acta Informatica.

[328]  David Gamarnik,et al.  Embracing the giant component , 2004, Random Struct. Algorithms.

[329]  One , 2004 .

[330]  Gregory L. McColm,et al.  Threshold Functions for Random Graphs on a Line Segment , 2004, Combinatorics, Probability and Computing.

[331]  Stefanie Gerke,et al.  K5-free subgraphs of random graphs , 2004, Random Struct. Algorithms.

[332]  Paul G. Spirakis,et al.  The Existence and Efficient Construction of Large Independent Sets in General Random Intersection Graphs , 2004, ICALP.

[333]  Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees , 2004, math/0401115.

[334]  Joel Friedman,et al.  A proof of Alon's second eigenvalue conjecture and related problems , 2004, ArXiv.

[335]  Tao Zhou,et al.  Maximal planar networks with large clustering coefficient and power-law degree distribution. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[336]  B. Prabhakar,et al.  Proofs of the Parisi and Coppersmith‐Sorkin random assignment conjectures , 2005 .

[337]  Oliver Riordan,et al.  The Small Giant Component in Scale-Free Random Graphs , 2005, Combinatorics, Probability and Computing.

[338]  Alan M. Frieze,et al.  Perfect matchings in random bipartite graphs with minimal degree at least 2 , 2005, Random Struct. Algorithms.

[339]  Hamed Hatami Random cubic graphs are not homomorphic to the cycle of size 7 , 2005, J. Comb. Theory, Ser. B.

[340]  Chen Avin,et al.  On the Cover Time of Random Geometric Graphs , 2005, ICALP.

[341]  Omer Giménez,et al.  Asymptotic enumeration and limit laws of planar graphs , 2005, math/0501269.

[342]  Nathan Linial,et al.  Random Lifts Of Graphs: Perfect Matchings , 2005, Comb..

[343]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[344]  Christos Faloutsos,et al.  Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication , 2005, PKDD.

[345]  Hsien-Kuei Hwang,et al.  Profiles of random trees: correlation and width of random recursive trees and binary search trees , 2005, Advances in Applied Probability.

[346]  Tamás F. Móri,et al.  The Maximum Degree of the Barabási–Albert Random Tree , 2005, Combinatorics, Probability and Computing.

[347]  Svante Janson,et al.  Asymptotic degree distribution in random recursive trees , 2005, Random Struct. Algorithms.

[348]  Van H. Vu,et al.  Spectral norm of random matrices , 2005, STOC '05.

[349]  Hunting for sharp thresholds , 2005, Random Struct. Algorithms.

[350]  Christina Goldschmidt,et al.  Random Recursive Trees and the Bolthausen-Sznitman Coalesent , 2005, math/0502263.

[351]  Colin McDiarmid,et al.  Random planar graphs , 2005, J. Comb. Theory B.

[352]  Michael Molloy,et al.  Cores in random hypergraphs and Boolean formulas , 2005, Random Struct. Algorithms.

[353]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[354]  Alan M. Frieze,et al.  The Cover Time of Random Regular Graphs , 2005, SIAM J. Discret. Math..

[355]  Asaf Nachmias,et al.  The critical random graph, with martingales , 2005 .

[356]  Jerzy Szymanski Concentration of vertex degrees in a scale-free random graph process , 2005, Random Struct. Algorithms.

[357]  Zsolt Katona Width of a scale-free tree , 2005 .

[358]  Bhaskar Krishnamachari,et al.  Monotone properties of random geometric graphs have sharp thresholds , 2003, math/0310232.

[359]  Tibor Szabó,et al.  Positional games on random graphs , 2006, Random Struct. Algorithms.

[360]  Tatyana S. Turova Phase Transitions in Dynamical Random Graphs , 2006 .

[361]  A. Martin-Löf,et al.  Generating Simple Random Graphs with Prescribed Degree Distribution , 2006, 1509.06985.

[362]  Ilkka Norros,et al.  On a conditionally Poissonian graph process , 2006, Advances in Applied Probability.

[363]  Johan Wästlund AN EASY PROOF OF THE ζ ( 2 ) LIMIT IN THE RANDOM ASSIGNMENT PROBLEM , 2006 .

[364]  Jerzy Jaworski,et al.  The degree of a typical vertex in generalized random intersection graph models , 2006, Discret. Math..

[365]  Randomly coloring sparse random graphs with fewer colors than the maximum degree , 2006, Random Struct. Algorithms.

[366]  Nathan Linial,et al.  Random Lifts of Graphs: Edge Expansion , 2006, Comb. Probab. Comput..

[367]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[368]  Lili Rong,et al.  High-dimensional random Apollonian networks , 2005, cond-mat/0502591.

[369]  Tom Bohman,et al.  Creating a Giant Component , 2006, Comb. Probab. Comput..

[370]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[371]  Zsolt Katona Levels of a scale-free tree , 2006, Random Struct. Algorithms.

[372]  Hsien-Kuei Hwang,et al.  WIDTH AND MODE OF THE PROFILE FOR SOME RANDOM TREES OF LOGARITHMIC HEIGHT , 2006, math/0607119.

[373]  Nathan Linial,et al.  Homological Connectivity Of Random 2-Complexes , 2006, Comb..

[374]  Fan Chung Graham,et al.  The Volume of the Giant Component of a Random Graph with Given Expected Degrees , 2006, SIAM J. Discret. Math..

[376]  Simon Tavaré,et al.  A Tale of Three Couplings: Poisson–Dirichlet and GEM Approximations for Random Permutations , 2006, Combinatorics, Probability and Computing.

[377]  Hsien-Kuei Hwang,et al.  Profiles of Random Trees: Limit Theorems for Random Recursive Trees and Binary Search Trees , 2006, Algorithmica.

[378]  Konstantinos Panagiotou,et al.  Extremal subgraphs of random graphs , 2007, SODA '07.

[379]  Vijaya Ramachandran,et al.  The diameter of sparse random graphs , 2007, Random Struct. Algorithms.

[380]  Bálint Tóth,et al.  Random trees and general branching processes , 2007, Random Struct. Algorithms.

[381]  Michael Behrisch,et al.  Component Evolution in Random Intersection Graphs , 2007, Electron. J. Comb..

[382]  Joel Ratsaby,et al.  The VC dimension of k-uniform random hypergraphs , 2007, Random Struct. Algorithms.

[383]  Hsien-Kuei Hwang,et al.  Profiles of random trees: Plane‐oriented recursive trees , 2007, Random Struct. Algorithms.

[384]  Joel H. Spencer,et al.  Birth control for giants , 2007, Comb..

[385]  Alan M. Frieze,et al.  On the Chromatic Number of Random Graphs with a Fixed Degree Sequence , 2007, Comb. Probab. Comput..

[386]  Helmut Prodinger,et al.  Level of nodes in increasing trees revisited , 2007, Random Struct. Algorithms.

[387]  Edward R. Scheinerman,et al.  Random Dot Product Graph Models for Social Networks , 2007, WAW.

[388]  Alan M. Frieze,et al.  A Geometric Preferential Attachment Model of Networks , 2006, Internet Math..

[389]  Alan M. Frieze,et al.  The cover time of the preferential attachment graph , 2007, J. Comb. Theory, Ser. B.

[390]  Xuding Zhu,et al.  The Map-Coloring Game , 2007, Am. Math. Mon..

[391]  F. Frances Yao,et al.  k-Nearest-Neighbor Clustering and Percolation Theory , 2007, Algorithmica.

[392]  Anusch Taraz,et al.  K4-free subgraphs of random graphs revisited , 2007, Comb..

[393]  Béla Bollobás,et al.  The phase transition in inhomogeneous random graphs , 2007, Random Struct. Algorithms.

[394]  Alan M. Frieze,et al.  Randomly generated intersecting hypergraphs II , 2016, Random Struct. Algorithms.

[395]  Tom Bohman,et al.  Randomly generated intersecting hypergraphs II , 2007 .

[396]  Nicholas C. Wormald,et al.  Colouring Random 4-Regular Graphs , 2007, Combinatorics, Probability and Computing.

[397]  Elchanan Mossel,et al.  Gibbs rapidly samples colorings of G(n, d/n) , 2007, 0707.3241.

[398]  Benny Sudakov,et al.  On the value of a random minimum length , 2007 .

[399]  Svante Janson,et al.  Monotonicity, asymptotic normality and vertex degrees in random graphs , 2007 .

[400]  B. Sudakov,et al.  Minors in Expanding Graphs , 2007, 0707.0133.

[401]  H. Prodinger,et al.  Level of nodes in increasing trees revisited , 2007 .

[402]  Alois Panholzer,et al.  On the degree distribution of the nodes in increasing trees , 2007, J. Comb. Theory, Ser. A.

[403]  V. Ramachandran,et al.  The diameter of sparse random graphs , 2007 .

[404]  Boris G. Pittel,et al.  On the Number of Fixed Pairs in a Random Instance of the Stable Marriage Problem , 2007, SIAM J. Discret. Math..

[405]  Svante Janson,et al.  Rainbow Hamilton cycles in random regular graphs , 2007, Random Struct. Algorithms.

[406]  Abraham D. Flaxman,et al.  The Lower Tail of the Random Minimum Spanning Tree , 2007, Electron. J. Comb..

[407]  R. Durrett Random Graph Dynamics: References , 2006 .

[408]  Mohammad Mahdian,et al.  Stochastic Kronecker Graphs , 2007, WAW.

[409]  Svante Janson,et al.  A simple solution to the k-core problem , 2007, Random Struct. Algorithms.

[410]  Allan Sly,et al.  Cutoff phenomena for random walks on random regular graphs , 2008, 0812.0060.

[411]  Andreas N. Lagerås,et al.  Epidemics on Random Graphs with Tunable Clustering , 2007, Journal of Applied Probability.

[412]  Anthony Bonato,et al.  A Spatial Web Graph Model with Local Influence Regions , 2007, Internet Math..

[413]  Daniela Kühn,et al.  The order of the largest complete minor in a random graph , 2007, Random Struct. Algorithms.

[414]  Christos Faloutsos,et al.  Dynamics of large networks , 2008 .

[415]  Percolation in the k-nearest neighbor graph , 2008 .

[416]  Tobias Müller Two-point concentration in random geometric graphs , 2008, Comb..

[417]  J. Beck Combinatorial Games: Tic-Tac-Toe Theory , 2008 .

[418]  Jerzy Jaworski,et al.  Random mappings with exchangeable in‐degrees , 2008, Random Struct. Algorithms.

[419]  Alan M. Frieze,et al.  The cover time of the giant component of a random graph , 2008, Random Struct. Algorithms.

[420]  Alan M. Frieze,et al.  A new approach to the planted clique problem , 2008, FSTTCS.

[421]  Alex Scott On the concentration of the chromatic number of random graphs , 2008 .

[422]  Stephen J. Young,et al.  Random dot product graphs: a flexible model for complex networks , 2008 .

[423]  Noga Alon,et al.  The Probabilistic Method, Third Edition , 2008, Wiley-Interscience series in discrete mathematics and optimization.

[424]  H. van den Esker A geometric preferential attachment model with fitness , 2008 .

[425]  Hosam M. Mahmoud,et al.  Phase Changes in Subtree Varieties in Random Recursive and Binary Search Trees , 2008, SIAM J. Discret. Math..

[426]  Pawe L Pra Lat CLEANING RANDOM GRAPHS WITH BRUSHES , 2008 .

[427]  Andreas N. Lagerås,et al.  A Note on the Component Structure in Random Intersection Graphs with Tunable Clustering , 2008, Electron. J. Comb..

[428]  T. Turova Asymptotics for the size of the largest component scaled to “logn” in inhomogeneous random graphs , 2008, 0812.3007.

[429]  Bruce A. Reed,et al.  The evolution of the mixing rate of a simple random walk on the giant component of a random graph , 2008, Random Struct. Algorithms.

[430]  T. Bohman The triangle-free process , 2008, 0806.4375.

[431]  Béla Bollobás,et al.  Handbook of large-scale random networks , 2008 .

[432]  Benny Sudakov,et al.  Local resilience of graphs , 2007, Random Struct. Algorithms.

[433]  Vojtech Rödl,et al.  An approximate Dirac-type theorem for k-uniform hypergraphs , 2008, Comb..

[434]  Anusch Taraz,et al.  The random planar graph process , 2008, Random Struct. Algorithms.

[435]  Noga Alon,et al.  Cleaning Regular Graphs with Brushes , 2008, SIAM J. Discret. Math..

[436]  N. Wormald,et al.  On the chromatic number of random d-regular graphs , 2008, 0812.2937.

[437]  Maria J. Serna,et al.  Walkers on the Cycle and the Grid , 2008, SIAM J. Discret. Math..

[438]  Alan M. Frieze,et al.  The game chromatic number of random graphs , 2008, Random Struct. Algorithms.

[439]  Roberto Di Pietro,et al.  Redoubtable Sensor Networks , 2008, TSEC.

[440]  Y. Peres,et al.  Critical random graphs: Diameter and mixing time , 2007, math/0701316.

[441]  Mindaugas Bloznelis Degree distribution of a typical vertex in a general random intersection graph , 2008 .

[442]  Raphael Yuster,et al.  On Rainbow Connection , 2008, Electron. J. Comb..

[443]  Michael Krivelevich,et al.  On two Hamilton cycle problems in random graphs , 2008 .

[444]  Svante Janson Plane recursive trees, Stirling permutations and an urn model , 2008 .

[445]  Jerzy Jaworski,et al.  The Vertex Degree Distribution of Passive Random Intersection Graph Models , 2008, Combinatorics, Probability and Computing.

[446]  József Balogh,et al.  Erdős–Ko–Rado in Random Hypergraphs , 2009, Combinatorics, Probability and Computing.

[447]  Benny Sudakov,et al.  Avoiding small subgraphs in Achlioptas processes , 2007, Random Struct. Algorithms.

[448]  Navin Goyal,et al.  Expanders via random spanning trees , 2008, SODA.

[449]  Fabrizio Grandoni,et al.  Balanced cut approximation in random geometric graphs , 2009, Theor. Comput. Sci..

[450]  Mikko Alava,et al.  Branching Processes , 2009, Encyclopedia of Complexity and Systems Science.

[451]  Pawel Pralat AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 43 (2009), Pages 237–251 Cleaning random graphs with brushes , 2022 .

[452]  Johan Wästlund An easy proof of the $\zeta(2)$ limit in the random assignment problem , 2009 .

[453]  Tibor Szabó,et al.  Asymptotic random graph intuition for the biased connectivity game , 2009, Random Struct. Algorithms.

[454]  Victor M. Preciado,et al.  Spectral analysis of virus spreading in random geometric networks , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[455]  Anusch Taraz,et al.  Coloring Random Intersection Graphs and Complex Networks , 2008, SIAM J. Discret. Math..

[456]  Mindaugas Bloznelis,et al.  Component evolution in a secure wireless sensor network , 2009, Networks.

[457]  Boris G. Pittel,et al.  On the Likely Number of Solutions for the Stable Marriage Problem , 2009, Combinatorics, Probability and Computing.

[458]  B. Bollobás,et al.  A critical constant for the k nearest-neighbour model , 2007, Advances in Applied Probability.

[459]  Willemien Kets,et al.  RANDOM INTERSECTION GRAPHS WITH TUNABLE DEGREE DISTRIBUTION AND CLUSTERING , 2009, Probability in the Engineering and Informational Sciences.

[460]  Adam Wierman,et al.  Generalizing Kronecker graphs in order to model searchable networks , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[461]  Alan M. Frieze,et al.  Hamilton cycles in 3-out , 2009, Random Struct. Algorithms.

[462]  Amin Coja-Oghlan,et al.  Graph Partitioning via Adaptive Spectral Techniques , 2009, Combinatorics, Probability and Computing.

[463]  Stefanie Gerke,et al.  Connectivity of the uniform random intersection graph , 2008, Discret. Math..

[464]  L. Harris,et al.  The Scottish Book Mathematics from the Scottish Cafe , 2010 .

[465]  Dmitri V. Krioukov,et al.  Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces , 2008, 2010 Proceedings IEEE INFOCOM.

[466]  Nicolas W. Hengartner,et al.  Component Evolution in General Random Intersection Graphs , 2010, WAW.

[467]  Alois Panholzer,et al.  Ordered increasing k-trees: Introduction and analysis of a preferential attachment network model , 2010 .

[468]  Katarzyna Rybarczyk,et al.  Poisson Approximation of the Number of Cliques in Random Intersection Graphs , 2010, Journal of Applied Probability.

[469]  Mindaugas Bloznelis,et al.  The Largest Component in an Inhomogeneous Random Intersection Graph with Clustering , 2010, Electron. J. Comb..

[470]  Benny Sudakov,et al.  Resilient Pancyclicity of Random and Pseudorandom Graphs , 2009, SIAM J. Discret. Math..

[471]  Hosam M. Mahmoud The Power of Choice in the Construction of Recursive Trees , 2010 .

[472]  Boris Pittel On a random graph evolving by degrees , 2010 .

[473]  Adam Wierman,et al.  Distance-Dependent Kronecker Graphs for Modeling Social Networks , 2010, IEEE Journal of Selected Topics in Signal Processing.

[474]  Svante Janson,et al.  On the Number of Perfect Matchings in Random Lifts , 2009, Combinatorics, Probability and Computing.

[475]  Alan M. Frieze,et al.  A note on the random greedy triangle-packing algorithm , 2010, ArXiv.

[476]  Alan M. Frieze,et al.  Anti-Ramsey properties of random graphs , 2010, J. Comb. Theory, Ser. B.

[477]  W. T. Gowers,et al.  Combinatorial theorems in sparse random sets , 2010, 1011.4310.

[478]  Benny Sudakov,et al.  Local Resilience and Hamiltonicity Maker–Breaker Games in Random Regular Graphs , 2009, Combinatorics, Probability and Computing.

[479]  Tomasz Luczak,et al.  Two critical periods in the evolution of random planar graphs , 2010, 1006.0444.

[480]  Thomas Sauerwald,et al.  Efficient broadcast on random geometric graphs , 2010, SODA '10.

[481]  Christos Faloutsos,et al.  Kronecker Graphs: An Approach to Modeling Networks , 2008, J. Mach. Learn. Res..

[482]  T. F. Móri,et al.  Local Degree Distribution in Scale Free Random Graphs , 2010, 1007.4314.

[483]  Mindaugas Bloznelis,et al.  A random intersection digraph: Indegree and outdegree distributions , 2010, Discret. Math..

[484]  Alan M. Frieze,et al.  Hamilton Cycles in Random Graphs with a Fixed Degree Sequence , 2010, SIAM J. Discret. Math..

[485]  Alan M. Frieze,et al.  Loose Hamilton Cycles in Random 3-Uniform Hypergraphs , 2010, Electron. J. Comb..

[486]  Michael Molloy,et al.  The scaling window for a random graph with a given degree sequence , 2009, SODA '10.

[487]  Alan M. Frieze,et al.  Finding a maximum matching in a sparse random graph in O(n) expected time , 2008, JACM.

[488]  N. Alon,et al.  Increasing the chromatic number of a random graph , 2010 .

[489]  Tomasz Luczak,et al.  Chasing robbers on random graphs: Zigzag theorem , 2010, Random Struct. Algorithms.

[490]  G. Brightwell,et al.  Vertices of high degree in the preferential attachment tree , 2010, 1012.5550.

[491]  Benny Sudakov,et al.  Hamiltonicity thresholds in Achlioptas processes , 2008, Random Struct. Algorithms.

[492]  David Gamarnik,et al.  Combinatorial approach to the interpolation method and scaling limits in sparse random graphs , 2010, STOC '10.

[493]  N. Wormald Models of random regular graphs , 2010 .

[494]  Rick Durrett,et al.  Probability: Theory and Examples, 4th Edition , 2010 .

[495]  Svante Janson,et al.  Asymptotic equivalence and contiguity of some random graphs , 2008, Random Struct. Algorithms.

[496]  A. Frieze,et al.  Component structure induced by a random walk on a random graph , 2010 .

[497]  Pawe,et al.  Cleaning random d-regular graphs with Brooms , 2010 .

[498]  Michael Krivelevich,et al.  The logic of random regular graphs , 2010 .

[499]  Amin Vahdat,et al.  Hyperbolic Geometry of Complex Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[500]  Yuval Peres,et al.  Anatomy of a young giant component in the random graph , 2009, Random Struct. Algorithms.

[501]  Katarzyna Rybarczyk,et al.  Diameter, connectivity, and phase transition of the uniform random intersection graph , 2011, Discret. Math..

[502]  Konstantinos Panagiotou,et al.  The multiple-orientability thresholds for random hypergraphs , 2011, SODA '11.

[503]  Michael Fuchs The Subtree Size Profile of Plane-oriented Recursive Trees , 2011, ANALCO.

[504]  Colin McDiarmid,et al.  On the chromatic number of random geometric graphs , 2011, Comb..

[505]  Pawel Pralat,et al.  Cleaning Random d-Regular Graphs with Brooms , 2011, Graphs Comb..

[506]  Paul G. Spirakis,et al.  On the independence number and Hamiltonicity of uniform random intersection graphs , 2011, Theor. Comput. Sci..

[507]  Katarzyna Rybarczyk,et al.  Equivalence of a random intersection graph and G(n,p) , 2009, Random Struct. Algorithms.

[508]  Alan M. Frieze,et al.  High Degree Vertices, Eigenvalues and Diameter of Random Apollonian Networks , 2011, ArXiv.

[509]  Michael Krivelevich,et al.  Submitted to the Annals of Applied Probability HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS By , 2010 .

[510]  Benny Sudakov,et al.  On the Resilience of Hamiltonicity and Optimal Packing of Hamilton Cycles in Random Graphs , 2011, SIAM J. Discret. Math..

[511]  Cristopher Moore,et al.  Independent Sets in Random Graphs from the Weighted Second Moment Method , 2010, APPROX-RANDOM.

[512]  Nicholas C. Wormald,et al.  Disjoint Hamilton cycles in the random geometric graph , 2009, J. Graph Theory.

[513]  Rory Wilson,et al.  Geometric Graph Properties of the Spatial Preferred Attachment model , 2011, ArXiv.

[514]  Katarzyna Rybarczyk,et al.  Sharp Threshold Functions for Random Intersection Graphs via a Coupling Method , 2011, Electron. J. Comb..

[515]  Alan M. Frieze,et al.  Component structure of the vacant set induced by a random walk on a random graph , 2011, SODA '11.

[516]  Mindaugas Bloznelis,et al.  A note on Hamiltonicity of uniform random intersection graphs , 2011 .

[517]  Svante Janson,et al.  Generalized Stirling permutations, families of increasing trees and urn models , 2008, J. Comb. Theory, Ser. A.

[518]  Gesine Reinert,et al.  The shortest distance in random multi‐type intersection graphs , 2010, Random Struct. Algorithms.

[519]  Thomas Sauerwald,et al.  Diameter and Broadcast Time of Random Geometric Graphs in Arbitrary Dimensions , 2011, Algorithmica.

[520]  Blair D. Sullivan,et al.  A mathematical analysis of the R‐MAT random graph generator , 2011, Networks.

[521]  Konstantinos Panagiotou,et al.  Sharp load thresholds for cuckoo hashing , 2009, Random Struct. Algorithms.

[522]  Benny Sudakov,et al.  Dirac's theorem for random graphs , 2012, Random Struct. Algorithms.

[523]  David Bruce Wilson,et al.  A sharp threshold for minimum bounded-depth/diameter spanning and Steiner trees , 2008 .

[524]  Wei Chen,et al.  On the Hyperbolicity of Small-World and Treelike Random Graphs , 2012, Internet Math..

[525]  Michael Krivelevich,et al.  Sharp threshold for the appearance of certain spanning trees in random graphs , 2012, Random Struct. Algorithms.

[526]  Jonathan Jordan Geometric preferential attachment in non-uniform metric spaces , 2012 .

[527]  Y. Peres,et al.  Mixing time of near-critical random graphs , 2009, 0908.3870.

[528]  Alan M. Frieze,et al.  Cover time of a random graph with given degree sequence , 2012, Discret. Math..

[529]  Wojciech Samotij,et al.  Optimal Packings of Hamilton Cycles in Sparse Random Graphs , 2011, SIAM J. Discret. Math..

[530]  Jeff Kahn,et al.  Tight upper tail bounds for cliques , 2011, Random Struct. Algorithms.

[531]  Svante Janson,et al.  Susceptibility in Inhomogeneous Random Graphs , 2009, Electron. J. Comb..

[532]  Alan M. Frieze,et al.  Stationary distribution and cover time of random walks on random digraphs , 2012, J. Comb. Theory, Ser. B.

[533]  Oliver Riordan,et al.  The Hitting Time of Rainbow Connection Number Two , 2012, Electron. J. Comb..

[534]  Armand M. Makowski,et al.  Zero–One Laws for Connectivity in Random Key Graphs , 2009, IEEE Transactions on Information Theory.

[535]  Michael Krivelevich,et al.  Hitting time results for Maker‐Breaker games , 2010, Random Struct. Algorithms.

[536]  Alan M. Frieze,et al.  Maximum matchings in random bipartite graphs and the space utilization of Cuckoo Hash tables , 2009, Random Struct. Algorithms.

[537]  Sanjeev Khanna,et al.  The Power of Local Information in Social Networks , 2012, WINE.

[538]  Rainbow Connection of Sparse Random Graphs , 2012, Electron. J. Comb..

[539]  Andrzej Dudek,et al.  Optimal Divisibility Conditions for Loose Hamilton Cycles in Random Hypergraphs , 2012, Electron. J. Comb..

[540]  Paul Horn,et al.  Giant components in Kronecker graphs , 2012, Random Struct. Algorithms.

[541]  Remco van der Hofstad,et al.  Weak disorder asymptotics in the stochastic mean-field model of distance , 2010, 1002.4362.

[542]  Luca Gugelmann,et al.  Random Hyperbolic Graphs: Degree Sequence and Clustering , 2012, ArXiv.

[543]  Friedrich Götze,et al.  Birth of a Strongly Connected Giant in an Inhomogeneous Random Digraph , 2012, J. Appl. Probab..

[544]  O. Riordan,et al.  Achlioptas process phase transitions are continuous , 2011, 1102.5306.

[545]  Domingos Dellamonica,et al.  An Improved Upper Bound on the Density of Universal Random Graphs , 2012, LATIN.

[546]  Jing He,et al.  On rainbow-k-connectivity of random graphs , 2010, Inf. Process. Lett..

[547]  Luc Devroye,et al.  Depth Properties of scaled attachment random recursive trees , 2012, Random Struct. Algorithms.

[548]  G. Reinert,et al.  Joint Vertex Degrees in the Inhomogeneous Random Graph Model ℊ(n,{pij }) , 2012, Advances in Applied Probability.

[549]  Nikolaos Fountoulakis,et al.  On the evolution of random graphs on spaces of negative curvature , 2012, ArXiv.

[550]  Alan M. Frieze,et al.  Rainbow Connectivity of Sparse Random Graphs , 2012, APPROX-RANDOM.

[551]  Daniela Kühn,et al.  On Pósa's Conjecture for Random Graphs , 2012, SIAM J. Discret. Math..

[552]  Mindaugas Bloznelis,et al.  Random Intersection Graph Process , 2013, Internet Math..

[553]  Dieter Mitsche,et al.  A Note on the Acquaintance Time of Random Graphs , 2013, Electron. J. Comb..

[554]  Erhard Godehardt,et al.  Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs , 2013, ECDA.

[555]  Erhard Godehardt,et al.  Recent Progress in Complex Network Analysis: Models of Random Intersection Graphs , 2013, ECDA.

[556]  Stephen J. Young,et al.  Connectivity and Giant Component of Stochastic Kronecker Graphs , 2013, ArXiv.

[557]  Béla Bollobás,et al.  Hereditary and Monotone Properties of Graphs , 2013, The Mathematics of Paul Erdős II.

[558]  Jirí Cerný,et al.  Critical window for the vacant set left by random walk on random regular graphs , 2011, Random Struct. Algorithms.

[559]  Valentas Kurauskas,et al.  Large cliques in sparse random intersection graphs (extended version) , 2013 .

[560]  Andrzej Dudek,et al.  Tight Hamilton cycles in random uniform hypergraphs , 2011, Random Struct. Algorithms.

[561]  Alan M. Frieze,et al.  On the Game Chromatic Number of Sparse Random Graphs , 2011, SIAM J. Discret. Math..

[562]  Michael Krivelevich,et al.  On the Number of Hamilton Cycles in Sparse Random Graphs , 2013, SIAM J. Discret. Math..

[563]  Pu Gao,et al.  On the Longest Paths and the Diameter in Random Apollonian Networks , 2013, Electron. Notes Discret. Math..

[564]  Alan M. Frieze,et al.  The cover times of random walks on random uniform hypergraphs , 2013, Theor. Comput. Sci..

[565]  Tamara G. Kolda,et al.  An in-depth analysis of stochastic Kronecker graphs , 2011, JACM.

[566]  Peter J. Cameron,et al.  The Random Graph , 2013, The Mathematics of Paul Erdős II.

[567]  Amin Coja-Oghlan,et al.  Chasing the k-colorability threshold , 2013 .

[568]  The triangle-free process and R(3,k) , 2013, 1302.6279.

[569]  Tom Bohman,et al.  Dynamic concentration of the triangle‐free process , 2013, Random Struct. Algorithms.

[570]  Valentas Kurauskas,et al.  On small subgraphs in a random intersection digraph , 2013, Discret. Math..

[571]  Benny Sudakov,et al.  The phase transition in random graphs: A simple proof , 2012, Random Struct. Algorithms.

[572]  Svante Janson,et al.  Protected nodes and fringe subtrees in some random trees , 2013, 1310.0665.

[573]  Nathan Ross,et al.  Degree asymptotics with rates for preferential attachment random graphs , 2013 .

[574]  Rory Wilson,et al.  Asymmetric Distribution of Nodes in the Spatial Preferred Attachment Model , 2013, WAW.

[575]  Amin Coja-Oghlan,et al.  Upper-Bounding the k-Colorability Threshold by Counting Covers , 2013, Electron. J. Comb..

[576]  Matthew Kahle Topology of random simplicial complexes: a survey , 2013, 1301.7165.

[577]  Joel H. Spencer,et al.  The Bohman‐Frieze process near criticality , 2011, Random Struct. Algorithms.

[578]  Mindaugas Bloznelis,et al.  Degree Distribution of an Inhomogeneous Random Intersection Graph , 2012, Electron. J. Comb..

[579]  Benny Sudakov,et al.  Longest cycles in sparse random digraphs , 2011, Random Struct. Algorithms.

[580]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[581]  Remco van der Hofstad,et al.  Critical behavior in inhomogeneous random graphs , 2009, Random Struct. Algorithms.

[582]  Jerzy Jaworski,et al.  Predecessors and Successors in Random Mappings with Exchangeable In-Degrees , 2013, Journal of Applied Probability.

[583]  R. Adamczak,et al.  Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order , 2013, 1304.1826.

[584]  Mindaugas Bloznelis,et al.  Perfect matchings in random intersection graphs , 2013 .

[585]  Robin Wilson,et al.  Modern Graph Theory , 2013 .

[586]  Tatyana S. Turova,et al.  Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1. , 2009, Random Struct. Algorithms.

[587]  Pu Gao,et al.  Arboricity and spanning-tree packing in random graphs with an application to load balancing , 2013, SODA.

[588]  Benny Sudakov,et al.  Cores of random graphs are born Hamiltonian , 2013, 1303.3524.

[589]  Ralph Keusch,et al.  The Game Chromatic Number of Dense Random Graphs , 2014, Electron. J. Comb..

[590]  Oliver Riordan Long cycles in random subgraphs of graphs with large minimum degree , 2014, Random Struct. Algorithms.

[591]  Katarzyna Rybarczyk,et al.  Constructions of independent sets in random intersection graphs , 2014, Theor. Comput. Sci..

[592]  Michel BodeNikolaos FountoulakisTobias Muller,et al.  The probability that the hyperbolic random graph is connected , 2014 .

[593]  Andrzej Dudek,et al.  An Alternative Proof of the Linearity of the Size-Ramsey Number of Paths , 2015, Comb. Probab. Comput..

[594]  Mindaugas Bloznelis,et al.  K-connectivity of Uniform S-intersection Graphs , 2014, Discret. Math..

[595]  Charilaos Efthymiou MCMC sampling colourings and independent sets of G(n, d/n) near uniqueness threshold , 2014, SODA.

[596]  Mihyun Kang,et al.  Properties of stochastic Kronecker graphs , 2014 .

[597]  Asaf Ferber,et al.  Packing a randomly edge-colored random graph with rainbow $k$-outs , 2014, 1410.1803.

[598]  S. Janson,et al.  Limit Laws for Functions of Fringe trees for Binary Search Trees and Recursive Trees , 2014, 1406.6883.

[599]  Tobias Müller,et al.  A threshold for the Maker-Breaker clique game , 2014, Random Struct. Algorithms.

[600]  Arran Hamm,et al.  On Erd\H{o}s-Ko-Rado for random hypergraphs II , 2014 .

[601]  Richard Montgomery,et al.  Sharp threshold for embedding combs and other spanning trees in random graphs , 2014, 1405.6560.

[602]  Alan M. Frieze,et al.  Looking for vertex number one , 2014, ArXiv.

[603]  Andrzej Dudek,et al.  Loose Hamilton Cycles in Regular Hypergraphs , 2015, Comb. Probab. Comput..

[604]  Alan M. Frieze,et al.  Cover time of a random graph with a degree sequence II: Allowing vertices of degree two , 2014, Random Struct. Algorithms.

[605]  R. Montgomery Embedding bounded degree spanning trees in random graphs , 2014, 1405.6559.

[606]  Nicholas C. Wormald,et al.  The mixing time of the giant component of a random graph , 2006, Random Struct. Algorithms.

[607]  Daniel Poole,et al.  On Weak Hamiltonicity of a Random Hypergraph , 2014, 1410.7446.

[608]  Alan M. Frieze,et al.  Some Typical Properties of the Spatial Preferred Attachment Model , 2014, Internet Math..

[609]  Angelika Steger,et al.  A Short Proof of the Random Ramsey Theorem , 2014, Combinatorics, Probability and Computing.

[610]  Michael Krivelevich,et al.  Positional Games , 2014, 1404.2731.

[611]  Rushmir Mahmutćehajić Paths , 2014, The Science of Play.

[612]  Tom Bohman,et al.  The independent neighborhoods process , 2014, 1407.7192.

[613]  Alan M. Frieze,et al.  On a greedy 2‐matching algorithm and Hamilton cycles in random graphs with minimum degree at least three , 2011, Random Struct. Algorithms.

[614]  Luc Devroye,et al.  Connectivity of inhomogeneous random graphs , 2012, Random Struct. Algorithms.

[615]  Eyal Lubetzky,et al.  Cycle Factors and Renewal Theory , 2014, 1401.2707.

[616]  Jean Bertoin Sizes of the largest clusters for supercritical percolation on random recursive trees , 2014, Random Struct. Algorithms.

[617]  Alan M. Frieze,et al.  Rainbow hamilton cycles in random graphs , 2010, Random Struct. Algorithms.

[618]  G. Hooghiemstra,et al.  Universality for first passage percolation on sparse uniform and rank-1 random graphs , 2014 .

[619]  Andrzej Dudek,et al.  The t-Tone Chromatic Number of Random Graphs , 2012, Graphs Comb..

[620]  Tomasz Luczak,et al.  Hamilton cycles in random lifts of graphs , 2013, Eur. J. Comb..

[621]  Andrzej Dudek,et al.  Rainbow Connection of Random Regular Graphs , 2015, SIAM J. Discret. Math..

[622]  Alan M. Frieze,et al.  An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three , 2012, Random Struct. Algorithms.

[623]  D. Romik The Surprising Mathematics of Longest Increasing Subsequences , 2015 .

[624]  J. Bertoin,et al.  Supercritical percolation on large scale-free random trees , 2012, 1212.2333.

[625]  Benny Sudakov,et al.  Long paths and cycles in random subgraphs of graphs with large minimum degree , 2012, Random Struct. Algorithms.

[626]  Nikolaos Fountoulakis,et al.  On the Largest Component of a Hyperbolic Model of Complex Networks , 2015, Electron. J. Comb..

[627]  Daniela Kühn,et al.  Edge‐disjoint Hamilton cycles in random graphs , 2011, Random Struct. Algorithms.

[628]  A. Wade,et al.  Phase Transitions for Random Geometric Preferential Attachment Graphs , 2013, Advances in Applied Probability.

[629]  Alan M. Frieze,et al.  On-line List Colouring of Random Graphs , 2015, Electron. J. Comb..

[630]  Michael Krivelevich,et al.  Biased games on random boards , 2012, Random Struct. Algorithms.

[631]  Svante Janson,et al.  Limit laws for functions of fringe trees for binary search trees and random recursive trees , 2015 .

[632]  Angelika Steger,et al.  An algorithmic framework for obtaining lower bounds for random Ramsey problems extended abstract , 2015, SODA.

[633]  Jun Zhao,et al.  On k-Connectivity and Minimum Vertex Degree in Random s-Intersection Graphs , 2015, ANALCO.

[634]  Tobias Friedrich,et al.  Cliques in hyperbolic random graphs , 2015, INFOCOM.

[635]  Alan M. Frieze,et al.  Power of k Choices and Rainbow Spanning Trees in Random Graphs , 2015, Electron. J. Comb..

[636]  Dieter Mitsche,et al.  A Bound for the Diameter of Random Hyperbolic Graphs , 2015, ANALCO.

[637]  Alan M. Frieze,et al.  Long Paths in Random Apollonian Networks , 2014, Internet Math..

[638]  Alan M. Frieze,et al.  Between 2- and 3-Colorability , 2015, Electron. J. Comb..

[639]  Alan M. Frieze,et al.  On the Length of a Random Minimum Spanning Tree , 2012, Combinatorics, Probability and Computing.

[640]  Boris Pittel,et al.  Distance between two random k-out digraphs, with and without preferential attachment , 2013, Advances in Applied Probability.

[641]  Jeff Kahn,et al.  Mantel's theorem for random graphs , 2012, Random Struct. Algorithms.

[642]  Bobby DeMarco,et al.  Turán's Theorem for random graphs , 2015 .

[643]  Asaf Ferber,et al.  Closing Gaps in Problems related to Hamilton Cycles in Random Graphs and Hypergraphs , 2015, Electron. J. Comb..

[644]  Alan M. Frieze,et al.  Efficient algorithms for three-dimensional axial and planar random assignment problems , 2015, Random Struct. Algorithms.

[645]  Tom Bohman,et al.  A note on the random greedy independent set algorithm , 2013, Random Struct. Algorithms.

[646]  Angelika Steger,et al.  On the threshold for the Maker-Breaker H-game , 2016, Random Struct. Algorithms.

[647]  Remco van der Hofstad,et al.  Random Graphs and Complex Networks , 2016, Cambridge Series in Statistical and Probabilistic Mathematics.

[648]  Jeff Kahn,et al.  The threshold for combs in random graphs , 2014, Random Struct. Algorithms.

[649]  Andrzej Dudek,et al.  The set chromatic number of random graphs , 2016, Discret. Appl. Math..

[650]  Benny Sudakov,et al.  Some Remarks on Rainbow Connectivity , 2016, J. Graph Theory.

[651]  Nikolaos Fountoulakis,et al.  University of Birmingham Clustering and the hyperbolic geometry of complex networks , 2015 .

[652]  Ueli Peter,et al.  Universality of random graphs and rainbow embedding , 2013, Random Struct. Algorithms.

[653]  M. Schacht Extremal results for random discrete structures , 2016, 1603.00894.

[654]  Nicholas C. Wormald,et al.  Longest paths in random Apollonian networks and largest r-ary subtrees of random d-ary recursive trees , 2016, J. Appl. Probab..

[655]  Andrew Thomason,et al.  Online containers for hypergraphs, with applications to linear equations , 2016, J. Comb. Theory, Ser. B.

[656]  Benny Sudakov,et al.  Random directed graphs are robustly Hamiltonian , 2014, Random Struct. Algorithms.

[657]  Alan M. Frieze,et al.  Rainbow matchings and Hamilton cycles in random graphs , 2013, Random Struct. Algorithms.

[658]  C. Harris,et al.  Diameter , 2016, Definitions.

[659]  Dudley Stark,et al.  Poisson approximation of counts of subgraphs in random intersection graphs , 2016, 1609.01699.

[660]  Andrzej Dudek,et al.  Acquaintance Time of Random Graphs Near Connectivity Threshold , 2016, SIAM J. Discret. Math..

[661]  Alexis Darrasse,et al.  Shape Measures of Random Increasing k-trees † , 2016, Combinatorics, Probability and Computing.

[662]  Alan M. Frieze,et al.  On random k-out subgraphs of large graphs , 2017, Random Struct. Algorithms.

[663]  Valentas Kurauskas,et al.  Large Cliques in Sparse Random Intersection Graphs , 2013, Electron. J. Comb..

[664]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[665]  On the connectedness of random hypergraphs , 2017 .

[666]  Andrzej Dudek,et al.  Embedding the Erdős-Rényi hypergraph into the random regular hypergraph and Hamiltonicity , 2015, J. Comb. Theory, Ser. B.

[667]  Santosh S. Vempala,et al.  Statistical Algorithms and a Lower Bound for Detecting Planted Cliques , 2012, J. ACM.

[668]  Asaf Ferber,et al.  Packing, counting and covering Hamilton cycles in random directed graphs , 2017 .

[669]  Abbas Mehrabian Justifying the small-world phenomenon via random recursive trees , 2017, Random Struct. Algorithms.

[670]  Katarzyna Rybarczyk The Coupling Method for Inhomogeneous Random Intersection Graphs , 2017, Electron. J. Comb..

[671]  Yufei Zhao,et al.  On the variational problem for upper tails in sparse random graphs , 2014, Random Struct. Algorithms.

[672]  Yury Person,et al.  An algorithmic framework for obtaining lower bounds for random Ramsey problems , 2014, J. Comb. Theory, Ser. B.

[673]  Remco van der Hofstad,et al.  Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs , 2014, Journal of Statistical Physics.

[674]  Jeff Kahn,et al.  On Erdős-Ko-Rado for Random Hypergraphs II , 2019, Comb. Probab. Comput..