Geodesic
Symmetrized and continuous generalization of transversals
Mathematica Bohemica, Tome 121 (1996) no. 1, pp. 95-106

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MR Zbl
The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.
The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.
DOI : 10.21136/MB.1996.125937
Classification : 05B35, 05D15, 52B40, 90C35
Keywords: transversal; polymatroid; system of representatives 
Kochol, Martin. Symmetrized and continuous generalization of transversals. Mathematica Bohemica, Tome 121 (1996) no. 1, pp. 95-106. doi: 10.21136/MB.1996.125937
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[1] M. Aigner: Combinatorial Theory. Springer, Berlin, 1979. | MR | Zbl

[2] R. A. Brualdi: Common transversals and strong exchange systems. J. Combin. Theory Ser. B 3 (1970), 307-329. | MR | Zbl

[3] J. Edmonds: Submodular functions, matroids and certain polyhedra. Combinatorial structures and their applications (R. Guy, H. Hanani, N. Sauer, J. Schonheim, eds.). Gordon and Breach, New York, 1970, pp. 69-87. | MR | Zbl

[4] J. Edmonds D. R. Fulkerson: Transversals and matroid partitions. J. Res. Nat. Bur. Standards Sect. B 69 (1965), 147-153. | MR

[5] M. Grötschel L. Lovász A. Schrijver: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin, 1988. | MR

[6] P. Hall: On representatives of subsets. J. London Math. Soc. 10 (1935), 26-30. | DOI | Zbl

[7] P. Horák: Transversals and matroids. Topics in Combinatorics and Graph Theory (R. Bodendiek, R. Henn, eds.). Physica-Verlag, Heidelberg, 1990, pp. 381-389. | MR

[8] M. Kochol: The notion and basic properties of M-transversals. Discrete Math. 104 (1991), 191-196. | DOI | MR

[9] M. Kochol: About a generalization of transversals. Math. Bohem. 119 (1994), 143-149. | MR | Zbl

[10] M. Kochol: Some generalizations of transversal theory. CSc. thesis, Bratislava, 1990. (In Slovak.)

[11] E. L. Lawler C. U. Martel: Computing maximal "polymatroidal" network flows. Math. Oper. Research 7 (1982), 334-347. | DOI | MR

[12] C. J. H. McDiarmid: Rado's theorem for polymatroids. Proc. Cambridge Phil. Soc. 18 (1975), 263-281. | MR | Zbl

[13] L. Mirsky: Transversal Theory. Academic Press, London, 1971. | MR | Zbl

[14] L. Mirsky H. Perfect: Applications of the notion of independence to combinatorial analysis. J. Combin. Theory 2 (1967), 327-357. | DOI | MR

[15] H. Perfect: Independence spaces and combinatorial problems. Proc. London Math. Soc. 19 (1969), 17-30. | DOI | MR | Zbl

[16] S. Poljak: Personal communication. | Zbl

[17] R. Rado: A theorem on independence relations. Quart. J. Math. (Oxford) 13 (1942), 83-89. | DOI | MR | Zbl

[18] A. Recski: Matroid Theory and its Applications in Electric Network Theory and in Statics. Springer, Berlin, 1989. | MR | Zbl

[19] A. Schrijver: Total dual integrality from directed graphs, crossing families, and sub- and supermodular functions. Progress in Combinatorial Optimization (W. R. Pulleyblank, ed.). Academic Press, Toronto, 1984, pp. 315-362. | MR | Zbl

[20] D. J. A. Welsh: Matroid Theory. Academic Press, London, 1976. | MR | Zbl

[21] D. R. Woodall: Vector transversals. J. Combin. Theory Ser. B 32 (1982), 189-205. | DOI | MR | Zbl

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