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arXiv · 1203.2171

K_6 minors in 6-connected graphs of bounded tree-width

Ken-ichi Kawarabayashi·Serguei Norine·Robin Thomas·Paul Wollan
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Abstract

We prove that every sufficiently big 6-connected graph of bounded tree-width either has a K_6 minor, or has a vertex whose deletion makes the graph planar. This is a step toward proving that the same conclusion holds for all sufficiently big 6-connected graphs. Jorgensen conjectured that it holds for all 6-connected graphs.

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Ken-ichi Kawarabayashi, Serguei Norine, Robin Thomas, Paul Wollan. 2013-04-05. K_6 minors in 6-connected graphs of bounded tree-width. https://arxiv.org/abs/1203.2171

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