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arXiv · 1807.01119

A short derivation of the structure theorem for graphs with excluded topological minors

Joshua Erde·Daniel Weißauer
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Abstract

As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph $H$ as a minor has a tree-decomposition in which each torso is almost embeddable in a surface of bounded genus. Recently, Grohe and Marx proved a similar result for graphs not containing $H$ as a topological minor. They showed that every graph which does not contain $H$ as a topological minor has a tree-decomposition in which every torso is either almost embeddable in a surface of bounded genus, or has a bounded number of vertices of high degree. We give a short proof of the theorem of Grohe and Marx, improving their bounds on a number of the parameters involved.

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Joshua Erde, Daniel Weißauer. 2018-07-03. A short derivation of the structure theorem for graphs with excluded topological minors. https://arxiv.org/abs/1807.01119

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