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http://dx.doi.org/10.5666/KMJ.2017.57.3.371

Expansion and Contraction Functors on Matriods  

Rahmati-Asghar, Rahim (Department of Mathematics, Faculty of Basic Sciences, University of Maragheh)
Publication Information
Kyungpook Mathematical Journal / v.57, no.3, 2017 , pp. 371-383 More about this Journal
Abstract
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.
Keywords
expansion functor; contraction functor; White's conjecture;
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