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

2016/09/10 by Rong Chen, Chen, Rong
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.1609.03049

openalex publication_date 2016/09/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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) 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 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.

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