| Title:
|
About a generalization of transversals (English) |
| Author:
|
Kochol, Martin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
143-149 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson. (English) |
| Keyword:
|
finite family of sets |
| Keyword:
|
transversal |
| Keyword:
|
matroid |
| Keyword:
|
system of representatives |
| MSC:
|
05B35 |
| MSC:
|
05D15 |
| idZBL:
|
Zbl 0806.05064 |
| idMR:
|
MR1293247 |
| DOI:
|
10.21136/MB.1994.126084 |
| . |
| Date available:
|
2009-09-24T21:04:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126084 |
| . |
| Reference:
|
[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. Zbl 0268.05019, MR 0270945 |
| Reference:
|
[2] J. Edmonds D. R. Fulkerson: Transversals and matroid partition.J. Res. Nat. Bur. Stand. 69B (1965), 147-153. MR 0188090 |
| Reference:
|
[3] L. R. Ford D. R. Fulkerson: Network flow and systems of representatives.Canad. J. Math. 10 (1958), 78-84. MR 0098039, 10.4153/CJM-1958-009-1 |
| Reference:
|
[4] P. Hall: On representatives of subsets.J. London Math. Soc. 10 (1935), 26-30. Zbl 0010.34503, 10.1112/jlms/s1-10.37.26 |
| Reference:
|
[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. Zbl 0299.05127, MR 0371691 |
| Reference:
|
[6] P. Horák: Transversals and matroids.Topics in Combinatorics and Graph Theory (Bodendiek, Henn, eds.). Physica-Veriag, Heidelberg, 1990, pp. 381-389. MR 1100058 |
| Reference:
|
[7] M. Kochol: The notion and basic properties of M-transversals.Discrete Math. 104 (1992), 191-196. Zbl 0769.05027, MR 1172847, 10.1016/0012-365X(92)90333-B |
| Reference:
|
[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. MR 0480111 |
| Reference:
|
[9] L. Lovász M. D. Plummer: Matching Theory.North-Holland, Amsterdam, 1986. |
| Reference:
|
[10] C. J. H. McDiarmid: Rado's theorem for polymatroids.Proc. Cambridge Phil. Soc. 78 (1975), 263-281. Zbl 0321.05028, MR 0379247 |
| Reference:
|
[11] L. Mirsky: Transversal Theory.Academic Press, London, 1971. Zbl 0282.05001, MR 0282853 |
| Reference:
|
[12] L. Mirsky H. Perfect: Applications of the notion of independence to combinatorial analysis.J. Combinatorial Theory 2 (1967), 327-357. MR 0225675, 10.1016/S0021-9800(67)80034-6 |
| Reference:
|
[13] H. Perfect: A generalization of Rado's theorem on independent transversals.Proc. Cambridge Phil. Soc. 66 (1969), 513-515. Zbl 0186.30303, MR 0244065 |
| Reference:
|
[14] R. Rado: A theorem on independence relations.Quart. J. Math. (Oxford) 13 (1942), 83-89. Zbl 0063.06369, MR 0008250, 10.1093/qmath/os-13.1.83 |
| Reference:
|
[15] D. J. A. Welsh: Transversal theory and matroids.Canad. J. Math. 21 (1969), 1323-1330. Zbl 0288.05019, MR 0252249, 10.4153/CJM-1969-145-0 |
| Reference:
|
[16] D. J. A. Welsh: Matroid Theory.Academic Press, London, 1976. Zbl 0343.05002, MR 0427112 |
| Reference:
|
[17] D. R. Woodall: Vector transversals.J. Combinatorial Theory (B) 32 (1982), 189-205. Zbl 0467.05024, MR 0657688, 10.1016/0095-8956(82)90035-1 |
| . |
