Excluded minors in cubic graphs

Neil Robertson; Paul Seymour; Robin Thomas

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arXiv · 1403.2118

Excluded minors in cubic graphs

Neil Robertson·Paul Seymour·Robin Thomas

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Abstract

Let G be a cubic graph, with girth at least five, such that for every partition X,Y of its vertex set with |X|,|Y|>6 there are at least six edges between X and Y. We prove that if there is no homeomorphic embedding of the Petersen graph in G, and G is not one particular 20-vertex graph, then either G\v is planar for some vertex v, or G can be drawn with crossings in the plane, but with only two crossings, both on the infinite region. We also prove several other theorems of the same kind.

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BibTeX RIS

Neil Robertson, Paul Seymour, Robin Thomas. 2014-03-09. Excluded minors in cubic graphs. https://arxiv.org/abs/1403.2118

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