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arXiv · 1609.03049

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

Rong Chen
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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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Rong Chen. 2016-09-10. The excluded minors for the class of matroids that are graphic or bicircular lift. https://arxiv.org/abs/1609.03049

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