2017/05/26 by Rahim Rahmati-Asghar, Rahmati-Asghar, Rahim
Computer Science · Mathematics · #05B35 #52B40 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.CO #msc:05B35 #msc:52B40
paper · pdf · doi:10.48550/arxiv.1705.09539
13 pages
arxiv created 2017/05/26 · openalex publication_date 2017/05/26 · arxiv updated 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.