About a generalization of transversals

Martin Kochol

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 2, page 143-149
  • ISSN: 0862-7959

Abstract

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The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.

How to cite

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Kochol, Martin. "About a generalization of transversals." Mathematica Bohemica 119.2 (1994): 143-149. <http://eudml.org/doc/29238>.

@article{Kochol1994,
abstract = {The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.},
author = {Kochol, Martin},
journal = {Mathematica Bohemica},
keywords = {finite family of sets; transversal; matroid; system of representatives; finite family of sets; transversal; matroid},
language = {eng},
number = {2},
pages = {143-149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {About a generalization of transversals},
url = {http://eudml.org/doc/29238},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Kochol, Martin
TI - About a generalization of transversals
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 2
SP - 143
EP - 149
AB - The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.
LA - eng
KW - finite family of sets; transversal; matroid; system of representatives; finite family of sets; transversal; matroid
UR - http://eudml.org/doc/29238
ER -

References

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  1. J. Edmonds, Submodular functions, matroids and certain polyhedra, Combinatorial Structures and Their Applications (Guy, Hanani, Sauer and Schönheim, eds.). Gordon and Branch, New York, 1970, pp. 69-87. (1970) Zbl0268.05019MR0270945
  2. J. Edmonds D. R. Fulkerson, Transversals and matroid partition, J. Res. Nat. Bur. Stand. 69B (1965), 147-153. (1965) MR0188090
  3. L. R. Ford D. R. Fulkerson, 10.4153/CJM-1958-009-1, Canad. J. Math. 10 (1958), 78-84. (1958) MR0098039DOI10.4153/CJM-1958-009-1
  4. P. Hall, 10.1112/jlms/s1-10.37.26, J. London Math. Soc. 10 (1935), 26-30. (1935) Zbl0010.34503DOI10.1112/jlms/s1-10.37.26
  5. T. Helgason, Aspects of the theory of hypermatroids, Hypergraph Seminar (Berge, Ray-Chaudhuri, eds.). Lecture Notes in Math. 411, Springer, Berlin, 1974, pp. 191-214. (1974) Zbl0299.05127MR0371691
  6. P. Horák, Transversals and matroids, Topics in Combinatorics and Graph Theory (Bodendiek, Henn, eds.). Physica-Veriag, Heidelberg, 1990, pp. 381-389. (1990) MR1100058
  7. M. Kochol, 10.1016/0012-365X(92)90333-B, Discrete Math. 104 (1992), 191-196. (1992) Zbl0769.05027MR1172847DOI10.1016/0012-365X(92)90333-B
  8. L. Lovász, Flats in matroids and geometric graphs, Combinatorial Surveys, Proc. Sixth British Combinatorial Conf. (Cameron, ed.). Academic Press, New York, 1977, pp. 45-86. (1977) MR0480111
  9. L. Lovász M. D. Plummer, Matching Theory, North-Holland, Amsterdam, 1986. (1986) 
  10. C. J. H. McDiarmid, Rado's theorem for polymatroids, Proc. Cambridge Phil. Soc. 78 (1975), 263-281. (1975) Zbl0321.05028MR0379247
  11. L. Mirsky, Transversal Theory, Academic Press, London, 1971. (1971) Zbl0282.05001MR0282853
  12. L. Mirsky H. Perfect, 10.1016/S0021-9800(67)80034-6, J. Combinatorial Theory 2 (1967), 327-357. (1967) MR0225675DOI10.1016/S0021-9800(67)80034-6
  13. H. Perfect, A generalization of Rado's theorem on independent transversals, Proc. Cambridge Phil. Soc. 66 (1969), 513-515. (1969) Zbl0186.30303MR0244065
  14. R. Rado, 10.1093/qmath/os-13.1.83, Quart. J. Math. (Oxford) 13 (1942), 83-89. (1942) Zbl0063.06369MR0008250DOI10.1093/qmath/os-13.1.83
  15. D. J. A. Welsh, 10.4153/CJM-1969-145-0, Canad. J. Math. 21 (1969), 1323-1330. (1969) Zbl0288.05019MR0252249DOI10.4153/CJM-1969-145-0
  16. D. J. A. Welsh, Matroid Theory, Academic Press, London, 1976. (1976) Zbl0343.05002MR0427112
  17. D. R. Woodall, 10.1016/0095-8956(82)90035-1, J. Combinatorial Theory (B) 32 (1982), 189-205. (1982) Zbl0467.05024MR0657688DOI10.1016/0095-8956(82)90035-1

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