Expansion and contraction functors on matriods

Autor:	Rahmati-Asghar, Rahim
Rok vydání:	2017
Předmět:	Mathematics - Combinatorics Mathematics - Commutative Algebra 05B35 52B40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1705.09539 Zobrazit plný text záznamu View this record from Arxiv