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arXiv · 2408.15335

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

Sandra Albrechtsen·Raphael W. Jacobs·Paul Knappe·Paul Wollan
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Abstract

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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Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Paul Wollan. 2025-11-18. A characterisation of graphs quasi-isometric to $K_4$-minor-free graphs. https://arxiv.org/abs/2408.15335

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