Geodesic
About a generalization of transversals
Mathematica Bohemica, Tome 119 (1994) no. 2, pp. 143-149

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.
The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.
DOI : 10.21136/MB.1994.126084
Classification : 05B35, 05D15
Keywords: finite family of sets; transversal; matroid; system of representatives 
Kochol, Martin. About a generalization of transversals. Mathematica Bohemica, Tome 119 (1994) no. 2, pp. 143-149. doi: 10.21136/MB.1994.126084
@article{10_21136_MB_1994_126084,
     author = {Kochol, Martin},
     title = {About a generalization of transversals},
     journal = {Mathematica Bohemica},
     pages = {143--149},
     year = {1994},
     volume = {119},
     number = {2},
     doi = {10.21136/MB.1994.126084},
     mrnumber = {1293247},
     zbl = {0806.05064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126084/}
}
TY  - JOUR
AU  - Kochol, Martin
TI  - About a generalization of transversals
JO  - Mathematica Bohemica
PY  - 1994
SP  - 143
EP  - 149
VL  - 119
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126084/
DO  - 10.21136/MB.1994.126084
LA  - en
ID  - 10_21136_MB_1994_126084
ER  - 
%0 Journal Article
%A Kochol, Martin
%T About a generalization of transversals
%J Mathematica Bohemica
%D 1994
%P 143-149
%V 119
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126084/
%R 10.21136/MB.1994.126084
%G en
%F 10_21136_MB_1994_126084

[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. | MR | Zbl

[2] J. Edmonds D. R. Fulkerson: Transversals and matroid partition. J. Res. Nat. Bur. Stand. 69B (1965), 147-153. | MR

[3] L. R. Ford D. R. Fulkerson: Network flow and systems of representatives. Canad. J. Math. 10 (1958), 78-84. | DOI | MR

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

[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. | MR | Zbl

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

[7] M. Kochol: The notion and basic properties of M-transversals. Discrete Math. 104 (1992), 191-196. | DOI | MR | Zbl

[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

[9] L. Lovász M. D. Plummer: Matching Theory. North-Holland, Amsterdam, 1986.

[10] C. J. H. McDiarmid: Rado's theorem for polymatroids. Proc. Cambridge Phil. Soc. 78 (1975), 263-281. | MR | Zbl

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

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

[13] H. Perfect: A generalization of Rado's theorem on independent transversals. Proc. Cambridge Phil. Soc. 66 (1969), 513-515. | MR | Zbl

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

[15] D. J. A. Welsh: Transversal theory and matroids. Canad. J. Math. 21 (1969), 1323-1330. | DOI | MR | Zbl

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

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

Cité par Sources :