Symmetrized and continuous generalization of transversals
Mathematica Bohemica (1996)
- Volume: 121, Issue: 1, page 95-106
- ISSN: 0862-7959
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topKochol, Martin. "Symmetrized and continuous generalization of transversals." Mathematica Bohemica 121.1 (1996): 95-106. <http://eudml.org/doc/247973>.
@article{Kochol1996,
abstract = {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.},
author = {Kochol, Martin},
journal = {Mathematica Bohemica},
keywords = {transversal; polymatroid; system of representatives; transversal; polymatroid},
language = {eng},
number = {1},
pages = {95-106},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Symmetrized and continuous generalization of transversals},
url = {http://eudml.org/doc/247973},
volume = {121},
year = {1996},
}
TY - JOUR
AU - Kochol, Martin
TI - Symmetrized and continuous generalization of transversals
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 1
SP - 95
EP - 106
AB - 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.
LA - eng
KW - transversal; polymatroid; system of representatives; transversal; polymatroid
UR - http://eudml.org/doc/247973
ER -
References
top- M. Aigner, Combinatorial Theory, Springer, Berlin, 1979. (1979) Zbl0415.05001MR0542445
- R. A. Brualdi, Common transversals and strong exchange systems, J. Combin. Theory Ser. B 3 (1970), 307-329. (1970) Zbl0194.00802MR0256887
- 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. (1970) Zbl0268.05019MR0270945
- J. Edmonds D. R. Fulkerson, Transversals and matroid partitions, J. Res. Nat. Bur. Standards Sect. B 69 (1965), 147-153. (1965) MR0188090
- M. Grötschel L. Lovász A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer, Berlin, 1988. (1988) MR0936633
- 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
- P. Horák, Transversals and matroids, Topics in Combinatorics and Graph Theory (R. Bodendiek, R. Henn, eds.). Physica-Verlag, Heidelberg, 1990, pp. 381-389. (1990) MR1100058
- M. Kochol, 10.1016/0012-365X(92)90333-B, Discrete Math. 104 (1991), 191-196. (1991) MR1172847DOI10.1016/0012-365X(92)90333-B
- M. Kochol, About a generalization of transversals, Math. Bohem. 119 (1994), 143-149. (1994) Zbl0806.05064MR1293247
- M. Kochol, Some generalizations of transversal theory, CSc. thesis, Bratislava, 1990. (In Slovak.) (1990)
- E. L. Lawler C. U. Martel, 10.1287/moor.7.3.334, Math. Oper. Research 7 (1982), 334-347. (1982) MR0667926DOI10.1287/moor.7.3.334
- C. J. H. McDiarmid, Rado's theorem for polymatroids, Proc. Cambridge Phil. Soc. 18 (1975), 263-281. (1975) Zbl0321.05028MR0379247
- L. Mirsky, Transversal Theory, Academic Press, London, 1971. (1971) Zbl0282.05001MR0282853
- L. Mirsky H. Perfect, 10.1016/S0021-9800(67)80034-6, J. Combin. Theory 2 (1967), 327-357. (1967) MR0225675DOI10.1016/S0021-9800(67)80034-6
- H. Perfect, 10.1112/plms/s3-19.1.17, Proc. London Math. Soc. 19 (1969), 17-30. (1969) Zbl0176.28302MR0241309DOI10.1112/plms/s3-19.1.17
- S. Poljak, [unknown], Personal communication. Zbl1167.05028
- 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
- A. Recski, Matroid Theory and its Applications in Electric Network Theory and in Statics, Springer, Berlin, 1989. (1989) Zbl0729.05012MR1027839
- 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. (1984) Zbl0542.90068MR0771885
- D. J. A. Welsh, Matroid Theory, Academic Press, London, 1976. (1976) Zbl0343.05002MR0427112
- D. R. Woodall, 10.1016/0095-8956(82)90035-1, J. Combin. Theory Ser. B 32 (1982), 189-205. (1982) Zbl0467.05024MR0657688DOI10.1016/0095-8956(82)90035-1
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