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Matching theory for combinatorial geometries. (English) Zbl 0218.05013


MSC:

05D15 Transversal (matching) theory
51D20 Combinatorial geometries and geometric closure systems
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References:

[1] Martin Aigner and Thomas A. Dowling, Matching theorems for combinatorial geometries, Bull. Amer. Math. Soc. 76 (1970), 57 – 60. · Zbl 0278.05022
[2] Claude Berge, Théorie des graphes et ses applications, Collection Universitaire de Mathématiques, II, Dunod, Paris, 1958 (French). · Zbl 0088.15404
[3] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1940; rev. ed., 1948, 1967. MR 1, 325; MR 10, 673. · Zbl 0063.00402
[4] Henry H. Crapo and Gian-Carlo Rota, On the foundations of combinatorial theory: Combinatorial geometries, Preliminary edition, The M.I.T. Press, Cambridge, Mass.-London, 1970. · Zbl 0231.05024
[5] Jack Edmonds, Submodular functions, matroids, and certain polyhedra, Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969) Gordon and Breach, New York, 1970, pp. 69 – 87. · Zbl 0268.05019
[6] L. Mirsky and Hazel Perfect, Applications of the notion of independence to problems of combinatorial analysis, J. Combinatorial Theory 2 (1967), 327 – 357. · Zbl 0153.02201
[7] Oystein Ore, Galois connexions, Trans. Amer. Math. Soc. 55 (1944), 493 – 513. · Zbl 0060.06204
[8] Oystein Ore, Graphs and matching theorems, Duke Math. J. 22 (1955), 625 – 639. · Zbl 0068.16301
[9] R. Rado, A theorem on independence relations, Quart. J. Math., Oxford Ser. 13 (1942), 83 – 89. · Zbl 0063.06369
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