与 $K_4$ 无小图准等距的图的特征描述

arXiv - MATH - Metric Geometry Pub Date : 2024-08-27 DOI:arxiv-2408.15335

Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Paul Wollan

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引用次数: 0

摘要

我们证明了存在一个函数 $f$，使得每个没有 $K$-fat$K_4$ 次要图的图都是 $f(K)$ 与没有 $K_4$ 次要图的图准等距。这解决了 Georgakopoulos 和 Papasoglu 的一般猜想中的 $K_4$ 情况。我们的证明技术还为藤原和 Papasoglu 首次建立的相应 $K_4^-$ 情况提供了新的简短证明。

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A characterisation of graphs quasi-isometric to $K_4$-minor-free graphs

We prove that there is a function $f$ such that every graph with no $K$-fat $K_4$ minor is $f(K)$-quasi-isometric to a graph with no $K_4$ minor. This solves the $K_4$-case of a general conjecture of Georgakopoulos and Papasoglu. Our proof technique also yields a new short proof of the respective $K_4^-$-case, which was first established by Fujiwara and Papasoglu.

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arXiv - MATH - Metric Geometry

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