The excluded minors for the class of matroids that are graphic or bicircular lift

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• 作者：Rong Chen ^{rongchen@fzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05B35 ; 05C22
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：83
• 期：Complete
• 页码：97-114
• 全文大小：413 K

文摘

Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph G  , the circuits of its bicircular lift matroid L(G)$L(G)$ are the edge sets of those subgraphs of G that contain at least two cycles, and are minimal with respect to this property. For each cycle C of G  , since L(G)/C$L(G)/C$ is graphic and most graphic matroids are not bicircular lift, the class of bicircular lift matroids is not minor-closed. In this paper, we prove that the class of matroids that are graphic or bicircular lift has a finite list of excluded minors.