Extensions and presentations of transversal matroids
A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections...
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| Vydané v: | European journal of combinatorics Ročník 50; s. 18 - 29 |
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| Hlavní autori: | , |
| Médium: | Journal Article Publikácia |
| Jazyk: | English |
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Elsevier Ltd
01.11.2015
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| ISSN: | 0195-6698, 1095-9971 |
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| Abstract | A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of M and extensions of presentations of M. We show that a presentation of M is minimal if and only if different extensions of it give different extensions of M; also, all transversal extensions of M can be obtained by extending the minimal presentations of M. We also begin to explore the partial order that the weak order gives on the transversal extensions of M. |
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| AbstractList | A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
Peer Reviewed A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of M and extensions of presentations of M. We show that a presentation of M is minimal if and only if different extensions of it give different extensions of M; also, all transversal extensions of M can be obtained by extending the minimal presentations of M. We also begin to explore the partial order that the weak order gives on the transversal extensions of M. |
| Author | de Mier, Anna Bonin, Joseph E. |
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| References | Mason (br000040) 1969 Brualdi (br000015) 1987; vol. 29 Oxley (br000045) 2011 Bondy, Welsh (br000010) 1971; 22 Brualdi, Dinolt (br000020) 1972; 12 Crapo (br000025) 1965; 69 Bondy (br000005) 1972; 5 Las Vergnas (br000035) 1970; 270 Edmonds, Fulkerson (br000030) 1965; 69B Las Vergnas (10.1016/j.ejc.2015.03.011_br000035) 1970; 270 Bondy (10.1016/j.ejc.2015.03.011_br000010) 1971; 22 Brualdi (10.1016/j.ejc.2015.03.011_br000020) 1972; 12 Mason (10.1016/j.ejc.2015.03.011_br000040) 1969 Oxley (10.1016/j.ejc.2015.03.011_br000045) 2011 Brualdi (10.1016/j.ejc.2015.03.011_br000015) 1987; vol. 29 Edmonds (10.1016/j.ejc.2015.03.011_br000030) 1965; 69B Bondy (10.1016/j.ejc.2015.03.011_br000005) 1972; 5 Crapo (10.1016/j.ejc.2015.03.011_br000025) 1965; 69 |
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| Title | Extensions and presentations of transversal matroids |
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