Expansion and contraction functors on matriods

Let \(M\) be a matroid. We study the expansions of \(M\) mainly to see how the combinatorial properties of \(M\) and its expansions are related to each other. It is shown that \(M\) is a graphic, binary or a transversal matroid if and only if an arbitrary expansion of \(M\) has the same property. Th...

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Bibliographic Details
Published inarXiv.org
Main Author Rahmati-Asghar, Rahim
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.05.2017
Subjects
Combinatorial analysis
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Summary:Let \(M\) be a matroid. We study the expansions of \(M\) mainly to see how the combinatorial properties of \(M\) and its expansions are related to each other. It is shown that \(M\) is a graphic, binary or a transversal matroid if and only if an arbitrary expansion of \(M\) has the same property. Then we introduce a new functor, called contraction, which acts in contrast to expansion functor. As a main result of paper, we prove that a matroid \(M\) satisfies White's conjecture if and only if an arbitrary expansion of \(M\) does. It follows that it suffices to focus on the contraction of a given matroid for checking whether the matroid satisfies White's conjecture. Finally, some classes of matroids satisfying White's conjecture are presented.
ISSN:2331-8422