Chapter V Polyhedral combinatorics

[1]  Giovanni Rinaldi,et al.  Facet identification for the symmetric traveling salesman polytope , 1990, Math. Program..

[2]  Egon Balas,et al.  The perfectly Matchable Subgraph Polytope of an arbitrary graph , 1989, Comb..

[3]  Manfred W. Padberg,et al.  A branch-and-cut approach to a traveling salesman problem with side constraints , 1989 .

[4]  Denis Naddef,et al.  The hirsch conjecture is true for (0, 1)-polytopes , 1989, Math. Program..

[5]  Yoshiko Wakabayashi,et al.  A cutting plane algorithm for a clustering problem , 1989, Math. Program..

[6]  William J. Cook,et al.  On cutting-plane proofs in combinatorial optimization , 1989 .

[7]  William R. Pulleyblank,et al.  König-Egerváry graphs, 2-bicritical graphs and fractional matchings , 1989, Discret. Appl. Math..

[8]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[9]  Martin Grötschel,et al.  An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design , 1988, Oper. Res..

[10]  Bernhard Fleischmann,et al.  A new class of cutting planes for the symmetric travelling salesman problem , 1988, Math. Program..

[11]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1988, Algorithms and Combinatorics.

[12]  Victor Klee,et al.  The d-Step Conjecture and Its Relatives , 1987, Math. Oper. Res..

[13]  László Lovász,et al.  Matching structure and the matching lattice , 1987, J. Comb. Theory, Ser. B.

[14]  Michele Conforti,et al.  A construction for binary matroids , 1987, Discret. Math..

[15]  Bert Gerards,et al.  Total dual integrality implies local strong unimodularity , 1987, Math. Program..

[16]  William R. Pulleyblank,et al.  Linear Systems for Constrained Matching Problems , 1987, Math. Oper. Res..

[17]  N. Maculan The Steiner Problem in Graphs , 1987 .

[18]  William R. Pulleyblank,et al.  Clique Tree Inequalities and the Symmetric Travelling Salesman Problem , 1986, Math. Oper. Res..

[19]  William H. Cunningham,et al.  Dominants and submissives of matching polyhedra , 1986, Math. Program..

[20]  Ali Ridha Mahjoub,et al.  On the cut polytope , 1986, Math. Program..

[21]  William J. Cook,et al.  On box totally dual integral polyhedra , 1986, Math. Program..

[22]  George L. Nemhauser,et al.  Simplex pivots on the set packing polytope , 1985, Math. Program..

[23]  Gérard Cornuéjols,et al.  The traveling salesman problem on a graph and some related integer polyhedra , 1985, Math. Program..

[24]  William H. Cunningham On submodular function minimization , 1985, Comb..

[25]  Gerhard Reinelt,et al.  A Cutting Plane Algorithm for the Linear Ordering Problem , 1984, Oper. Res..

[26]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[27]  William R. Pulleyblank,et al.  Hamiltonicity in (0-1)-polyhedra , 1984, J. Comb. Theory, Ser. B.

[28]  William H. Cunningham,et al.  Testing membership in matroid polyhedra , 1984, J. Comb. Theory, Ser. B.

[29]  L. Lovász,et al.  A POLYNOMIAL-TIME TEST FOR TOTAL DUAL INTEGRALITY IN FIXED DIMENSION , 1984 .

[30]  A. Schrijver Total Dual Integrality from Directed Graphs, Crossing Families, and Sub- and Supermodular Functions , 1984 .

[31]  Jack Edmonds,et al.  Reductions to 1-matching polyhedra , 1983, Networks.

[32]  Egon Balas,et al.  The perfectly matchable subgraph polytope of a bipartite graph , 1983, Networks.

[33]  William Cook A Minimal Totally Dual Integral Defining System for the b-Matching Polyhedron , 1983 .

[34]  Alexander Schrijver Short proofs on the matching polyhedron , 1983, J. Comb. Theory, Ser. B.

[35]  Rick Giles,et al.  Optimum matching forests III: Facets of matching forest polyhedra , 1982, Math. Program..

[36]  Rick Giles,et al.  Optimum matching forests II: General weights , 1982, Math. Program..

[37]  Rick Giles,et al.  Optimum matching forests I: Special weights , 1982, Math. Program..

[38]  Denis Naddef,et al.  Rank of maximum matchings in a graph , 1982, Math. Program..

[39]  F. Barahona,et al.  On the exact ground states of three-dimensional Ising spin glasses , 1982 .

[40]  László Lovász,et al.  Brick decompositions and the matching rank of graphs , 1982, Comb..

[41]  M. R. Rao,et al.  Odd Minimum Cut-Sets and b-Matchings , 1982, Math. Oper. Res..

[42]  M. Grötschel,et al.  New aspects of polyhedral theory , 1982 .

[43]  A. Hoffman Ordered Sets and Linear Programming , 1982 .

[44]  William R. Pulleyblank Total dual integrality and b-matchings , 1981, Oper. Res. Lett..

[45]  Alexander Schrijver,et al.  On total dual integrality , 1981 .

[46]  R. Chandrasekaran Polynomial Algorithms for Totally Dual Integral Systems and Extensions , 1981 .

[47]  Martin Grötschel,et al.  The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[48]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[49]  P. Seymour On Odd Cuts and Plane Multicommodity Flows , 1981 .

[50]  Richard M. Karp,et al.  On linear characterizations of combinatorial optimization problems , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[51]  Paul D. Seymour,et al.  Decomposition of regular matroids , 1980, J. Comb. Theory, Ser. B.

[52]  H. Crowder,et al.  Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality , 1980 .

[53]  Alexander Schrijver,et al.  On Cutting Planes , 1980 .

[54]  L. Khachiyan Polynomial algorithms in linear programming , 1980 .

[55]  Dirk Hausmann Adjacency on Polytopes in Combinatorial Optimization , 1980 .

[56]  Martin Grötschel,et al.  On the symmetric travelling salesman problem: Solution of a 120-city problem , 1980 .

[57]  Manfred W. Padberg,et al.  On the symmetric travelling salesman problem: A computational study , 1980 .

[58]  Alfred Lehman,et al.  On the width-length inequality , 1979, Math. Program..

[59]  Martin Grötschel,et al.  On the symmetric travelling salesman problem I: Inequalities , 1979, Math. Program..

[60]  Martin Grötschel,et al.  On the symmetric travelling salesman problem II: Lifting theorems and facets , 1979, Math. Program..

[61]  W. Pulleyblank,et al.  Total Dual Integrality and Integer Polyhedra , 1979 .

[62]  W. H. Cunningham,et al.  Theoretical Properties of the Network Simplex Method , 1979, Math. Oper. Res..

[63]  P. D. Seymour,et al.  On Multi‐Colourings of Cubic Graphs, and Conjectures of Fulkerson and Tutte , 1979 .

[64]  László Lovász,et al.  Graph Theory and Integer Programming , 1979 .

[65]  Klaus Truemper,et al.  Local unimodularity of matrix-vector pairs , 1978 .

[66]  Christos H. Papadimitriou,et al.  The adjacency relation on the traveling salesman polytope is NP-Complete , 1978, Math. Program..

[67]  C. Lucchesi,et al.  A Minimax Theorem for Directed Graphs , 1978 .

[68]  A. J. Hoffman,et al.  Local Unimodularity in the Matching Polytope , 1978 .

[69]  W. Cunningham,et al.  A primal algorithm for optimum matching , 1978 .

[70]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[71]  Martin Grötschel,et al.  Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme , 1977 .

[72]  J. Edmonds,et al.  A Min-Max Relation for Submodular Functions on Graphs , 1977 .

[73]  David B. Weinberger,et al.  Network Flows, Minimum Coverings, and the Four-Color Conjectures , 1976, Oper. Res..

[74]  V. Chvátal On certain polytopes associated with graphs , 1975 .

[75]  Alan J. Hoffman,et al.  A generalization of max flow—min cut , 1974, Math. Program..

[76]  M. R. Rao,et al.  The travelling salesman problem and a class of polyhedra of diameter two , 1974, Math. Program..

[77]  D. R. Fulkerson,et al.  On balanced matrices , 1974 .

[78]  J. Edmonds,et al.  Facets of I-matching polyhedra , 1974 .

[79]  Vasek Chvátal,et al.  Edmonds polytopes and weakly hamiltonian graphs , 1973, Math. Program..

[80]  Jack Edmonds,et al.  Matching, Euler tours and the Chinese postman , 1973, Math. Program..

[81]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[82]  Vasek Chvátal,et al.  Edmonds polytopes and a hierarchy of combinatorial problems , 1973, Discret. Math..

[83]  Egon Balas,et al.  On the Set-Covering Problem , 1972, Oper. Res..

[84]  Michel Balinski,et al.  Establishing the matching polytope , 1972 .

[85]  D. R. Fulkerson,et al.  Anti-blocking polyhedra , 1972 .

[86]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[87]  Jack Edmonds,et al.  Matroids and the greedy algorithm , 1971, Math. Program..

[88]  D. R. Fulkerson,et al.  Blocking and anti-blocking pairs of polyhedra , 1971, Math. Program..

[89]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[90]  D. Gale Optimal assignments in an ordered set: An application of matroid theory , 1968 .

[91]  D. Welsh Kruskal's theorem for matroids , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.

[92]  Jack Edmonds,et al.  Maximum matching and a polyhedron with 0,1-vertices , 1965 .

[93]  D. R. Fulkerson,et al.  Flows in networks , 1962 .

[94]  T. C. Hu,et al.  Multi-Terminal Network Flows , 1961 .

[95]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .

[96]  C Berge,et al.  TWO THEOREMS IN GRAPH THEORY. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[97]  R. Rado Note on Independence Functions , 1957 .

[98]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[99]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[100]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956, Canadian Journal of Mathematics.

[101]  William J. Cook,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, 50 Years of Integer Programming.

[102]  H. Raiffa,et al.  3. The Double Description Method , 1953 .

[103]  John von Neumann,et al.  1. A Certain Zero-sum Two-person Game Equivalent to the Optimal Assignment Problem , 1953 .

[104]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[105]  J. P. Secrétan,et al.  Der Saccus endolymphaticus bei Entzündungsprozessen , 1944 .

[106]  H. Whitney On the Abstract Properties of Linear Dependence , 1935 .

[107]  H. Weyl Elementare Theorie der konvexen Polyeder , 1934 .

[108]  C. Carathéodory Über den variabilitätsbereich der fourier’schen konstanten von positiven harmonischen funktionen , 1911 .

[109]  D. Hilbert Über die Theorie der algebraischen Formen , 1890 .