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

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 r...

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Veröffentlicht in:	arXiv.org 2024-08
Hauptverfasser:	Albrechtsen, Sandra, Jacobs, Raphael W, Knappe, Paul, Wollan, Paul
Format:	Artikel
Sprache:	eng
Schlagworte:	Graphs
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Zusammenfassung:	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.
ISSN:	2331-8422

Zusammenfassung:	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.
ISSN:	2331-8422

A characterisation of graphs quasi-isometric to \(K_4\)-minor-free graphs