Matroid decomposition

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[1]  Wen-Lian Hsu.  Decomposition of perfect graphs , 1987, J. Comb. Theory, Ser. B.

[2]  W. T. Tutte.  A homotopy theorem for matroids. II , 1958 .

[3]  Manfred W. Padberg,et al.  Perfect zero–one matrices , 1974, Math. Program..

[4]  Paul D. Seymour,et al.  Adjacency in Binary Matroids , 1986, Eur. J. Comb..

[5]  P. Vámos,et al.  The Missing Axiom of Matroid Theory is Lost Forever , 1978 .

[6]  Refael Hassin.  Solution Bases of Multiterminal Cut Problems , 1988, Math. Oper. Res..

[7]  James G. Oxley.  On singleton 1-rounded sets of matroids , 1984, J. Comb. Theory, Ser. B.

[8]  Klaus Truemper,et al.  On the Efficiency of Representability Tests for Matroids , 1982, Eur. J. Comb..

[9]  H. Watanabe,et al.  Topological degrees of freedom and mixed analysis of electrical networks , 1970 .

[10]  Appajosyula Satyanarayana,et al.  A Linear-Time Algorithm for Computing K-Terminal Reliability in Series-Parallel Networks , 1985, SIAM J. Comput..

[11]  Klaus Truemper,et al.  Max-Flow Min-Cut Matroids: Polynomial Testing and Polynomial Algorithms for Maximum Flow and Shortest Routes , 1987, Math. Oper. Res..

[12]  A. J. Hoffman.  The Role of Unimodularity in Applying Linear Inequalities to Combinatorial Theorems , 1979 .

[13]  J. Edmonds,et al.  A Combinatorial Decomposition Theory , 1980, Canadian Journal of Mathematics.

[14]  Satoru Fujishige.  A decomposition of distributive lattices , 1985, Discret. Math..

[15]  Gérard Cornuéjols,et al.  A Decomposition Theorem for Balanced Matrices , 1990, IPCO.

[16]  Robert E. Bixby,et al.  Converting Linear Programs to Network Problems , 1980, Math. Oper. Res..

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

[18]  Ali Ridha Mahjoub,et al.  Compositions of Graphs and Polyhedra III: Graphs with No W4 Minor , 1994, SIAM J. Discret. Math..

[19]  William H Cunningham,et al.  Improved Bounds for Matroid Partition and Intersection Algorithms , 1986, SIAM J. Comput..

[20]  Collette R. Coullard.  Counterexamples to conjectures on 4-connected matroids , 1986, Comb..

[21]  P. Seymour,et al.  Surveys in combinatorics 1985: Graph minors – a survey , 1985 .

[22]  Alfred Lehman,et al.  The Width-Length Inequality and Degenerate Projective Planes , 1990, Polyhedral Combinatorics.

[23]  C. Nash-Williams.  Decomposition of Finite Graphs Into Forests , 1964 .

[24]  L. Auslander,et al.  Incidence Matrices and Linear Graphs , 1959 .

[25]  I. Gitler.  Delta-wye-delta transformations: algorithms and applications , 1991 .

[26]  J. Edmonds.  Minimum partition of a matroid into independent subsets , 1965 .

[27]  William J. Lenhart,et al.  On the P4-structure of Perfect Graphs. IV. Partner graphs , 1990, J. Comb. Theory, Ser. B.

[28]  Wen-Lian Hsu,et al.  The coloring and maximum independent set problems on planar perfect graphs , 1988, JACM.

[29]  James G. Oxley.  On the matroids representable over GF(4) , 1986, J. Comb. Theory, Ser. B.

[30]  Tom Brylawski,et al.  A combinatorial model for series-parallel networks , 1971 .

[31]  László Lovász,et al.  Ear-decompositions of matching-covered graphs , 1983, Comb..

[32]  R. Bixby.  Recent Algorithms for Two Versions of Graph Realization and Remarks on Applications to Linear Programming , 1984 .

[33]  Jean Fonlupt,et al.  Compositions of Graphs and Polyhedra IV: Acyclic Spanning Subgraphs , 1994, SIAM J. Discret. Math..

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

[35]  Paul D. Seymour.  Packing and covering with matroid circuits , 1980, J. Comb. Theory, Ser. B.

[36]  M. Iri,et al.  Applications of Matroid Theory , 1982, ISMP.

[37]  L. Trotter,et al.  Integer Rounding and Polyhedral Decomposition for Totally Unimodular Systems , 1978 .

[38]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[39]  Jean Fonlupt,et al.  The traveling salesman problem in graphs with some excluded minors , 1992, Math. Program..

[40]  Mouloud Boulala,et al.  Polytope des independants d'un graphe serie-parallele , 1979, Discret. Math..

[41]  A. Satyanarayana,et al.  Network reliability analysis using 2-connected digraph reductions , 1985, Networks.

[42]  K. TRUEMPER,et al.  A decomposition theory for matroids III. Decomposition conditions , 1986, J. Comb. Theory, Ser. B.

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

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

[45]  P. Camion.  Characterization of totally unimodular matrices , 1965 .

[46]  S. Arnborg,et al.  Characterization and recognition of partial 3-trees , 1986 .

[47]  Wen-Lian Hsu,et al.  Recognizing circle graphs in polynomial time , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[48]  Wen-Lian Hsu.  Coloring planar perfect graphs by decomposition , 1986, Comb..

[49]  Donald K. Wagner,et al.  On theorems of Whitney and Tutte , 1985, Discret. Math..

[50]  Joseph P. S. Kung,et al.  Growth rates and critical exponents of classes of binary combinatorial geometries , 1986 .

[51]  S. Whitesides.  A Method for Solving Certain Graph Recognition and Optimization Problems, with Applications to Perfect Graphs , 1982 .

[52]  Toshihide Ibaraki,et al.  Strong unimodularity for matrices and hypergraphs , 1986, Discret. Appl. Math..

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

[54]  Paul D. Seymour,et al.  On minors of non-binary matroids , 1981, Comb..

[55]  Donald Keith Wagner.  An almost linear-time graph realization algorithm , 1983 .

[56]  E. L. Lawler,et al.  Flow Network Formulations of Polymatroid Optimization Problems , 1982 .

[57]  Thomas Zaslavsky,et al.  Biased graphs. I. Bias, balance, and gains , 1989, J. Comb. Theory, Ser. B.

[58]  R. Bixby.  A Composition for Perfect Graphs , 1984 .

[59]  Richard P. Anstee,et al.  Characterizations of Totally Balanced Matrices , 1984, J. Algorithms.

[60]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

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

[62]  Klaus Truemper,et al.  Alpha-balanced graphs and matrices and GF(3)-representability of matroids , 1982, J. Comb. Theory, Ser. B.

[63]  D. R. Fulkerson,et al.  On the Max Flow Min Cut Theorem of Networks. , 1955 .

[64]  Paul Seymour,et al.  Triples in Matroid Circuits , 1986, Eur. J. Comb..

[65]  Donald K. Wagner,et al.  Connectivity in bicircular matroids , 1985, J. Comb. Theory, Ser. B.

[66]  Talmage James Reid,et al.  Triangles in 3-connected matroids , 1991, Discret. Math..

[67]  W. Kern,et al.  Linear Programming Duality: An Introduction to Oriented Matroids , 1992 .

[68]  Thomas Inukai,et al.  Whitney Connectivity of Matroids , 1981 .

[69]  R. Halin.  Zur Theorie dern-fach zusammenhängenden Graphen , 1969 .

[70]  Kenneth R. Rebman.  Total unimodularity and the transportation problem: a generalization , 1974 .

[71]  Robert E. Tarjan,et al.  Dividing a Graph into Triconnected Components , 1973, SIAM J. Comput..

[72]  Aaron D. Wyner,et al.  Reliable Circuits Using Less Reliable Relays , 1993 .

[73]  James Oxley,et al.  The binary matroids with no 4-wheel minor , 1987 .

[74]  E. L. Lawler,et al.  Computing Maximal "Polymatroidal" Network Flows , 1982, Math. Oper. Res..

[75]  Jeff Kahn,et al.  A Geometric Approach to Forbidden Minors for GF(3) , 1984, J. Comb. Theory, Ser. A.

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

[77]  F. G. Commoner,et al.  A sufficient condition for a matrix to be totally unimodular , 1973, Networks.

[78]  Donald K. Wagner.  Equivalent factor matroids of graphs , 1988, Comb..

[79]  Paul D. Seymour,et al.  A note on nongraphic matroids , 1984, J. Comb. Theory, Ser. B.

[80]  A. Rosenthal,et al.  Transformations for simplifying network reliability calculations , 1977, Networks.

[81]  Günter M. Ziegler,et al.  Matroid representations and free arrangements , 1990 .

[82]  Stein Krogdahl.  The dependence graph for bases in matroids , 1977, Discret. Math..

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

[84]  L. Weinberg,et al.  GRAPH‐REALIZABILITY OF MATROIDS , 1979 .

[85]  L. Auslander,et al.  On the Realization of a Linear Graph Given Its Algebraic Specification , 1961 .

[86]  David P. Brown.  CIRCUIT AND UNIMODULAR MATRICES , 1976 .

[87]  K. Appel,et al.  Every Planar Map Is Four Colorable , 2019, Mathematical Solitaires & Games.

[88]  Kazuo Murota,et al.  Systems Analysis by Graphs and Matroids , 1987 .

[89]  K. Wagner.  Bemerkungen zu Hadwigers Vermutung , 1960 .

[90]  J.-C. Fournier.  A characterization of binary geometries by a double elimination axiom , 1981, J. Comb. Theory, Ser. B.

[91]  Alfred Lehman,et al.  A Solution of the Shannon Switching Game , 1964 .

[92]  Thomas Zaslavsky,et al.  The Geometry of Root Systems and Signed Graphs , 1981 .

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

[94]  Bert Gerards,et al.  A min-max relation for stable sets in graphs with no odd-K4 , 1989, J. Comb. Theory, Ser. B.

[95]  Klaus Truemper,et al.  Master polytopes for cycles of binary matroids , 1989 .

[96]  Siam J. CoMPtrr,et al.  FINDING A MAXIMUM CUT OF A PLANAR GRAPH IN POLYNOMIAL TIME * , 2022 .

[97]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[98]  Klaus Truemper,et al.  A decomposition theory for matroids. VI. Almost regular matroids , 1992, J. Comb. Theory, Ser. B.

[99]  W. T. Tutte.  An algorithm for determining whether a given binary matroid is graphic. , 1960 .

[100]  Manoel Lemos,et al.  K-Elimination property for circuits of matroids , 1991, J. Comb. Theory, Ser. B.

[101]  G. Dantzig,et al.  Integral Extreme Points , 1968 .

[102]  W. Cunningham.  Polyhedra for Composed Independence Systems , 1982 .

[103]  S. Fujishige.  Submodular systems and related topics , 1984 .

[104]  O. Ore.  The Four-Color Problem , 1967 .

[105]  Michele Conforti,et al.  North-Holland 23 Articulation sets in linear matrices I : forbidden perfect configurations and star cutsets * , 2001 .

[106]  F. Barahona.  The max-cut problem on graphs not contractible to K5 , 1983 .

[107]  Paul D. Seymour,et al.  On the connectivity function of a matroid , 1987, J. Comb. Theory, Ser. B.

[108]  Klaus Truemper,et al.  Decomposition and optimization over cycles in binary matroids , 1989, J. Comb. Theory, Ser. B.

[109]  Paul Seymour.  A FORBIDDEN MINOR CHARACTERIZATION OF MATROID PORTS , 1976 .

[110]  Robert E. Bixby,et al.  On Reid's characterization of the ternary matroids , 1979, J. Comb. Theory, Ser. B.

[111]  Klaus Truemper,et al.  On Whitney's 2-isomorphism theorem for graphs , 1980, J. Graph Theory.

[112]  Klaus Truemper,et al.  A decomposition theory for matroids. II. Minimal violation matroids , 1985, J. Comb. Theory, Ser. B.

[113]  W. T. Tutte,et al.  From Matrices to Graphs , 1964, Canadian Journal of Mathematics.

[114]  S. Akers.  The Use of Wye-Delta Transformations in Network Simplification , 1960 .

[115]  Clyde L. Monma,et al.  Sequencing with Series-Parallel Precedence Constraints , 1979, Math. Oper. Res..

[116]  Robert E. Bixby,et al.  On chains of 3-connected matroids , 1986, Discret. Appl. Math..

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

[118]  Kazuo Murota,et al.  Combinatorial canonical form of layered mixed matrices and its application to block-triangularization of systems of linear/nonlinear equations , 1987 .

[119]  Joseph A. Wald,et al.  Steiner trees in probabilistic networks , 1983 .

[120]  Thomas Zaslavsky,et al.  Biased graphs. II. The three matroids , 1991, J. Comb. Theory, Ser. B.

[121]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[122]  Satoru Fujishige,et al.  Submodular functions and optimization , 1991 .

[123]  James G. Oxley,et al.  On an excluded-minor class of matroids , 1990, Discret. Math..

[124]  Robert E. Bixby,et al.  ℓ-matrices and a Characterization of Binary Matroids , 1974, Discret. Math..

[125]  David P. Brown.  Compound and unimodular matrices , 1977, Discret. Math..

[126]  Eugene L. Lawler,et al.  Matroid intersection algorithms , 1975, Math. Program..

[127]  Jeff Kahn,et al.  On the Uniqueness of Matroid Representations Over GF(4) , 1988 .

[128]  D. Koenig.  Theorie Der Endlichen Und Unendlichen Graphen , 1965 .

[129]  James G. Oxley,et al.  Extensions of Tutte's wheels-and-whirls theorem , 1992, J. Comb. Theory, Ser. B.

[130]  G. Dirac.  A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs , 1952 .

[131]  M. Iri.  The maximum-rank minimum-term-rank theorem for the pivotal transforms of a matrix , 1969 .

[132]  R. Halin,et al.  Über einen Satz von K. Wagner zum Vierfarbenproblem , 1964 .

[133]  Thomas Zaslavsky,et al.  Balanced decompositions of a signed graph , 1987, J. Comb. Theory, Ser. B.

[134]  Louis Weinberg,et al.  The principal minors of a matroid , 1971 .

[135]  Tom Brylawski,et al.  A decomposition for combinatorial geometries , 1972 .

[136]  Günter M. Ziegler,et al.  Binary Supersolvable Matroids and Modular Constructions , 1991 .

[137]  James G. Oxley,et al.  The regular matroids with no 5-wheel minor , 1989, J. Comb. Theory, Ser. B.

[138]  Joseph P. S. Kung.  Excluding the Cycle Geometries of the Kuratowski Graphs from Binary Geometries , 1987 .

[139]  J. Fonlupt,et al.  Orientation of matrices , 1984 .

[140]  Themistocles Politof,et al.  Network Reliability and Inner-Four-Cycle-Free Graphs , 1986, Math. Oper. Res..

[141]  Amh Bert Gerards.  A short proof of Tutte's characterization of totally unimodular matrices , 1989 .

[142]  Vasek Chvátal,et al.  Star-cutsets and perfect graphs , 1985, J. Comb. Theory, Ser. B.

[143]  J. Oxley.  On 3-Connected Matroids , 1981, Canadian Journal of Mathematics.

[144]  Charles J. Colbourn,et al.  On two dual classes of planar graphs , 1990, Discret. Math..

[145]  András Frank,et al.  Submodular functions in graph theory , 1993, Discret. Math..

[146]  Refael Hassin.  Minimum cost flow with set-constraints , 1982, Networks.

[147]  Bernhard Korte,et al.  Complexity of Matroid Property Algorithms , 1982, SIAM J. Comput..

[148]  Robert E. Bixby,et al.  A short proof of the Truemper-Tseng theorem on max-flow min-cut matroids , 1989 .

[149]  William H. Cunningham,et al.  Separating cocircuits in binary matroids , 1982 .

[150]  Robert E. Bixby,et al.  Kuratowski's and Wagner's theorems for matroids , 1977, J. Comb. Theory, Ser. B.

[151]  T. Nishizeki,et al.  Necessary and sufficient condition for a graph to be three-terminal series-parallel , 1975 .

[152]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[153]  H. D. Ratliff,et al.  Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem , 1983, Oper. Res..

[154]  Paul D. Seymour,et al.  The matroids with the max-flow min-cut property , 1977, J. Comb. Theory B.

[155]  Rafael Hassin.  An algorithm for computing maximum solution bases , 1990 .

[156]  Masao Iri,et al.  A REVIEW OF RECENT WORK IN JAPAN ON PRINCIPAL PARTITIONS OF MATROIDS AND THEIR APPLICATIONS 1 , 1979 .

[157]  I. Heller,et al.  14 . An Extension of a Theorem of Dantzig’s , 1957 .

[158]  Paul Seymour,et al.  On Tutte's extension of the four-colour problem , 1981, J. Comb. Theory, Ser. B.

[159]  A. Tamir,et al.  On totally unimodular matrices , 1976, Networks.

[160]  Arthur M. Farley,et al.  Networks immune to isolated line failures , 1982, Networks.

[161]  Nobuji Saito,et al.  Linear-time computability of combinatorial problems on series-parallel graphs , 1982, JACM.

[162]  Eugene L. Lawler,et al.  Linear-Time Computation of Optimal Subgraphs of Decomposable Graphs , 1987, J. Algorithms.

[163]  W. T. Tutte.  Introduction to the theory of matroids , 1971 .

[164]  F. Harary,et al.  Planar Permutation Graphs , 1967 .

[165]  Paul D. Seymour,et al.  Minors of 3-Connected Matroids , 1985, Eur. J. Comb..

[166]  Alexander Schrijver,et al.  Min-Max Results in Combinatorial Optimization , 1982, ISMP.

[167]  Paul Seymour,et al.  On forbidden minors for (3) , 1988 .

[168]  Robert E. Bixby,et al.  Finding a small 3-connected minor maintaining a fixed minor and a fixed element , 1987, Comb..

[169]  Tom Brylawski,et al.  Modular constructions for combinatorial geometries , 1975 .

[170]  R. Bixby,et al.  A composition for matroids , 1975 .

[171]  G. Rota,et al.  On The Foundations of Combinatorial Theory: Combinatorial Geometries , 1970 .

[172]  R. Chandrasekaran.  Total Unimodularity of Matrices , 1969 .

[173]  M. Burlet,et al.  Polynomial algorithm to recognize a Meyniel graph , 1984 .

[174]  W. T. Tutte.  On the Problem of Decomposing a Graph into n Connected Factors , 1961 .

[175]  Neil Robertson,et al.  Minimal cyclic-4-connected graphs , 1984 .

[176]  Paul D. Seymour,et al.  Graph minors. VI. Disjoint paths across a disc , 1986, J. Comb. Theory, Ser. B.

[177]  W. T. Tutte.  Connectivity in Matroids , 1966, Canadian Journal of Mathematics.

[178]  Saunders MacLane,et al.  Some Interpretations of Abstract Linear Dependence in Terms of Projective Geometry , 1936 .

[179]  K. Truemper,et al.  Minimal Forbidden Subgraphs of Unimodular Multicommodity Networks , 1979, Math. Oper. Res..

[180]  Michele Conforti,et al.  Structural properties and recognition of restricted and strongly unimodular matrices , 1987, Math. Program..

[181]  Dominique de Werra,et al.  On some characterisations of totally unimodular matrices , 1981, Math. Program..

[182]  Robin J. Wilson.  Introduction to Graph Theory , 1974 .

[183]  R. Halin.  Zur Klassifikation der endlichen Graphen nach H. Hadwiger und K. Wagner , 1967 .

[184]  Klaus Truemper,et al.  Complement total unimodularity , 1980 .

[185]  William J. Lenhart,et al.  Two-colourings that decompose perfect graphs , 1990, J. Comb. Theory, Ser. B.

[186]  Klaus Truemper,et al.  Polynomial algorithms for a class of linear programs , 1981, Math. Program..

[187]  D. Barnette.  On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs , 1969 .

[188]  A. Hoffman,et al.  On unimodular matrices , 1962 .

[189]  A. Lehman.  Wye-Delta Transformation in Probablilistic Networks , 1963 .

[190]  Carsten Thomassen,et al.  Planarity and duality of finite and infinite graphs , 1980, J. Comb. Theory, Ser. B.

[191]  Paul D. Seymour,et al.  On Lehman's Width-Length Characterization , 1990, Polyhedral Combinatorics.

[192]  R. Bixby,et al.  A strengthened form of Tutte's characterization of regular matroids , 1976 .

[193]  Collette R. Coullard,et al.  On the complexity of recognizing a class of generalized networks , 1985 .

[194]  William H. Cunningham.  On matroid connectivity , 1981, J. Comb. Theory, Ser. B.

[195]  K. Menger.  Zur allgemeinen Kurventheorie , 1927 .

[196]  Klaus Truemper,et al.  A decomposition of the matroids with the max-flow min-cut property , 1986, Discret. Appl. Math..

[197]  Michele Conforti,et al.  Articulation sets in linear perfect matrices II: the wheel theorem and clique articulations , 1992, Discret. Math..

[198]  D. R. Fulkerson,et al.  Transversals and Matroid Partition , 1965 .

[199]  Paul D. Seymour,et al.  Graph minors. VIII. A kuratowski theorem for general surfaces , 1990, J. Comb. Theory, Ser. B.

[200]  Refael Hassin.  Multiterminal xcut problems , 1991, Ann. Oper. Res..

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

[202]  Klaus Truemper,et al.  A decomposition theory for matroids. V. Testing of matrix total unimodularity , 1990, J. Comb. Theory, Ser. B.

[203]  Paul Seymour,et al.  Detecting Matroid Minors , 1981 .

[204]  Michele Conforti,et al.  Structural properties and decomposition of linear balanced matrices , 1992, Math. Program..

[205]  Bert Gerards,et al.  Matrices with the edmonds—Johnson property , 1986, Comb..

[206]  Alexander K. Kelmans.  A short proof and a strengthening of the Whitney 2-isomorphism theorem on graphs , 1987, Discret. Math..

[207]  Klaus Truemper,et al.  On the delta-wye reduction for planar graphs , 1989, J. Graph Theory.

[208]  Paul D. Seymour,et al.  Matroid representation over GF(3) , 1979, J. Comb. Theory, Ser. B.

[209]  Charles J. Colbourn,et al.  Steiner trees, partial 2-trees, and minimum IFI networks , 1983, Networks.

[210]  D. Welsh,et al.  The computational complexity of matroid properties , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[211]  L. Hempel,et al.  A necessary and sufficient condition for the total unimodularity of a matrix in terms of graph theory , 1989 .

[212]  Claude Berge,et al.  Balanced matrices and property (G) , 1980 .

[213]  I. Cederbaum.  Matrices All of Whose Elements and Subdeterminants are 1, −1, or 0 , 1957 .

[214]  M. Kress,et al.  The use of jacobi's lemma in unimodularity theory , 1980, Math. Program..

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

[216]  Klaus Truemper,et al.  Algebraic Characterizations of Unimodular Matrices , 1978 .

[217]  A. Ingleton.  A Note on Independence Functions and Rank , 1959 .

[218]  Joseph P. S. Kung,et al.  Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries , 1988, Graphs Comb..

[219]  Donald K. Wagner.  Forbidden subgraphs and graph decomposition , 1987, Networks.

[220]  Seiya Negami.  A characterization of 3-connected graphs containing a given graph , 1982, J. Comb. Theory, Ser. B.

[221]  Gérard Cornuéjols,et al.  The traveling salesman problem in graphs with 3-edge cutsets , 1985, JACM.

[222]  R. Bixby.  A simple theorem on 3-connectivity , 1982 .

[223]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[224]  J. Scott Provan,et al.  Delta-Wye Transformations and the Efficient Reduction of Two-Terminal Planar Graphs , 1993, Oper. Res..

[225]  Michele Conforti,et al.  On the geometric structure of independence systems , 1989, Math. Program..

[226]  Satoru Fujishige,et al.  An Efficient PQ-Graph Algorithm for Solving the Graph-Realization Problem , 1980, J. Comput. Syst. Sci..

[227]  M. Padberg.  Total unimodularity and the Euler-subgraph problem , 1988 .

[228]  W. H. Cunningham.  BINARY MATROID SUMS , 1979 .

[229]  Gian-Carlo ROTA.  COMBINATORIAL THEORY , OLD AND NEW by , 2022 .

[230]  M. Iri,et al.  Structural solvability of systems of equations —A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems— , 1985 .

[231]  J. Oxley.  On nonbinary 3-connected matroids , 1987 .

[232]  Arthur M. Farley,et al.  Networks immune to isolated failures , 1981, Networks.

[233]  Refael Hassin.  Simultaneous Solution of Families of Problems , 1990, SIGAL International Symposium on Algorithms.

[234]  David Hartvigsen,et al.  Recognizing max-flow min-cut path matrices , 1988 .

[235]  Paul D. Seymour,et al.  Graph minors. IV. Tree-width and well-quasi-ordering , 1990, J. Comb. Theory, Ser. B.

[236]  K. Truemper,et al.  Single Commodity Representation of Multicommodity Networks , 1980, SIAM J. Matrix Anal. Appl..

[237]  Robert E. Bixby,et al.  An Almost Linear-Time Algorithm for Graph Realization , 1988, Math. Oper. Res..

[238]  Michele Conforti,et al.  Odd cycles and matrices with integrality properties , 1989, Math. Program..

[239]  Lars Löfgren.  Irredundant and redundant Boolean branch-networks , 1959, IRE Trans. Inf. Theory.

[240]  H. Young.  A Quick Proof of Wagner's Equivalence Theorem , 1971 .

[241]  J. Kahn,et al.  Characteristic Sets of Matroids , 1982 .

[242]  Paul C. Kainen,et al.  The Four-Color Problem , 1977 .

[243]  M. Iri,et al.  Use of matroid theory in operations research, circuits and systems theory , 1981 .

[244]  T. Lazarson,et al.  The Representation Problem for Independence Functions , 1958 .

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

[246]  Talmage James Reid,et al.  A note on roundedness in 4-connected matroids , 1991, Discret. Math..

[247]  Paul D. Seymour,et al.  A note on the production of matroid minors , 1977, J. Comb. Theory, Ser. B.

[248]  T. Ozawa.  On the minimal graphs of a certain class of graphs , 1971 .

[249]  Roderick Gould.  Graphs and Vector Spaces , 1958 .

[250]  Arvind Rajan.  Algorithmic applications of connectivity and related topics in matroid theory , 1987 .

[251]  W. Sierpinski,et al.  Sur le probléme des courbes gauches en Topologie , 2022 .

[252]  Richard M. Karp,et al.  A simple derivation of Edmonds' algorithm for optimum branchings , 1971, Networks.

[253]  András Frank,et al.  Conservative weightings and ear-decompositions of graphs , 1990, Comb..

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

[255]  Joseph P. S. Kung,et al.  Numerically regular hereditary classes of combinatorial geometries , 1986 .

[256]  A. Satyanarayana,et al.  An O(|E|) Time Algorithm for Computing the Reliability of a Class of Directed Networks , 1984, Oper. Res..

[257]  Gérard Cornuéjols,et al.  Compositions for perfect graphs , 1985, Discret. Math..

[258]  Mihalis Yannakakis.  On a class of totally unimodular matrices , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[259]  James G. Oxley,et al.  A characterization of the ternary matroids with no M(K4)-minor , 1987, J. Comb. Theory, Ser. B.

[260]  Joseph P. S. Kung.  THE LONG-LINE GRAPH OF A COMBINATORIAL GEOMETRY. I. EXCLUDING M(K4) AND THE (q + 2)-POINT LINE AS MINORS , 1988 .

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

[262]  James G. Oxley,et al.  On fixing elements in matroid minors , 1989, Comb..

[263]  Arie Tamir,et al.  Totally balanced and totally unimodular matrices defined by center location problems , 1987, Discret. Appl. Math..

[264]  Talmage James Reid,et al.  The Smallest Rounded Sets of Binary Matroids , 1990, Eur. J. Comb..

[265]  László Lovász,et al.  Matroid matching and some applications , 1980, J. Comb. Theory, Ser. B.

[266]  K. Wagner.  Über eine Eigenschaft der ebenen Komplexe , 1937 .

[267]  Klaus Truemper.  On matroid separations of graphs , 1987, J. Graph Theory.

[268]  Michele Conforti,et al.  On the Facial Structure of Independence System Polyhedra , 1988, Math. Oper. Res..

[269]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[270]  Fritz Bock.  An algorithm to construct a minimum directed spanning tree in a directed network , 1971 .

[271]  Manfred W. Padberg,et al.  A note on the total unimodularity of matrices , 1976, Discret. Math..

[272]  M. Padberg.  Characterisations of Totally Unimodular, Balanced and Perfect Matrices , 1975 .

[273]  Klaus Truemper,et al.  A decomposition theory for matroids. VII. Analysis of minimal violation matrices , 1992, J. Comb. Theory, Ser. B.

[274]  R. Duffin.  Topology of series-parallel networks , 1965 .

[275]  Robert E. Bixby,et al.  Short Cocircuits in Binary Matroids , 1987, Eur. J. Comb..

[276]  Michel Las Vergnas,et al.  Orientability of matroids , 1978, J. Comb. Theory, Ser. B.

[277]  Ramaswamy Chandrasekaran,et al.  Total weak unimodularity: testing and applications , 1984, Discret. Math..

[278]  Klaus Truemper,et al.  Partial Matroid Representations , 1984, Eur. J. Comb..

[279]  Joseph P. S. Kung.  The long-line graph of a combinatorial geometry. II. Geometries representable over two fields of different characteristics , 1990, J. Comb. Theory, Ser. B.

[280]  Thomas Zaslavsky,et al.  Characterizations of signed graphs , 1981, J. Graph Theory.

[281]  J. Kahn,et al.  Varieties of combinatorial geometries , 1982 .

[282]  Carsten Thomassen,et al.  Whitney's 2-switching theorem, cycle spaces, and arc mappings of directed graphs , 1989, J. Comb. Theory, Ser. B.

[283]  Ali Ridha Mahjoub,et al.  Compositions of Graphs and Polyhedra II: Stable Sets , 1994, SIAM J. Discret. Math..

[284]  William R. Pulleyblank,et al.  On cycle cones and polyhedra , 1989 .

[285]  András Frank,et al.  A Weighted Matroid Intersection Algorithm , 1981, J. Algorithms.

[286]  Gérard Cornuéjols,et al.  Halin graphs and the travelling salesman problem , 1983, Math. Program..

[287]  A.M.H. Gerards.  Graphs and polyhedra binary spaces and cutting planes , 1988 .

[288]  Michele Conforti,et al.  Properties of balanced and perfect matrices , 1992, Math. Program..

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

[290]  W. Cunningham.  Decomposition of Directed Graphs , 1982 .

[291]  J. Oxley.  On a matroid generalization of graph connectivity , 1981 .

[292]  Paul D. Seymour,et al.  Matroids and Multicommodity Flows , 1981, Eur. J. Comb..

[293]  A. R. Mahjoub,et al.  On the stable set polytope of a series-parallel graph , 1988, Math. Program..

[294]  I. Heller.  On linear systems with integral valued solutions. , 1957 .

[295]  A. Recski.  Matroid theory and its applications in electric network theory and in statics , 1989 .

[296]  Satoru Fujishige.  Canonical decompositions of symmetric submodular systems , 1980, Graph Theory and Algorithms.

[297]  P. Seymour.  On Tutte's Characterization of Graphic Matroids , 1980 .

[298]  Ali Ridha Mahjoub,et al.  Compositions of Graphs and Polyhedra I: Balanced Induced Subgraphs and Acyclic Subgraphs , 1994, SIAM J. Discret. Math..

[299]  A. Hoffman.  Total unimodularity and combinatorial theorems , 1976 .

[300]  A. Satyanarayana,et al.  A linear-time algorithm to compute the reliability of planar cube-free networks , 1990 .

[301]  W. T. Tutte.  Connectivity in graphs , 1966 .

[302]  Marc Wagowski,et al.  Characterizations of ternary matroids in terms of circuit signatures , 1989, J. Comb. Theory, Ser. B.

[303]  James Oxley,et al.  A characterization of a class of non-binary matroids , 1990, J. Comb. Theory, Ser. B.

[304]  Nobuji Saito,et al.  Necessary and sufficient conditions for a graph to be three-terminal series-parallel-cascade , 1978, J. Comb. Theory, Ser. B.

[305]  Klaus Truemper,et al.  Unimodular matrices of flow problems with additional constraints , 1977, Networks.

[306]  Vasek Chvátal.  On the P4-structure of perfect graphs III. Partner decompositions , 1987, J. Comb. Theory, Ser. B.