Fat minors cannot be thinned (by quasi-isometries)
Combinatorics
2024-05-16 v1 Metric Geometry
Abstract
We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no -fat minor is quasi-isometric to a graph with no minor. Our counterexample is furthermore not quasi-isometric to a graph with no 2-fat minor or a length space with no minor. On the other hand, we show that the following weakening holds: any graph with no -fat minor is quasi-isometric to a graph with no -fat minor.
Cite
@article{arxiv.2405.09383,
title = {Fat minors cannot be thinned (by quasi-isometries)},
author = {James Davies and Robert Hickingbotham and Freddie Illingworth and Rose McCarty},
journal= {arXiv preprint arXiv:2405.09383},
year = {2024}
}
Comments
14 pages, 5 figures