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,et al. 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,et al. 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 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 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.