On the basis graph of a bicolored matroid

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• 作者：Ana Paulina Figueroa ; Eduardo Rivera-Campo
• 关键词：Basis Graph
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2009
• 出版时间：1 December 2009
• 年：2009
• 卷：35
• 期：Complete
• 页码：269-273
• 全文大小：172 K

文摘

The basis graph of a matroid M is the graph G(B(M)) whose vertex set is the set of basis of M and two basis B and B^′ are adjacent if the size of its symmetric difference is two. We say that :E(M)→{1,2} is an effective 2-coloring of M if is a surjective function. Let M be a matroid and and effective 2-coloring of M, we define the bicolor basis graph, G(B(M),) with respet to of a matroid M as the spanning subgraph of G(B(M)) such that two basis B and B^′ are adjacent if they are adjacent in G(B(M)) and the restriction of to their symmetric difference is effective. Our main result states that if M is a connected matroid and is an effective 2-coloring of M, then G(B(M),) is connected.