On Andreae's Ubiquity Conjecture
Combinatorics
2022-10-11 v2
Abstract
A graph is ubiquitous if for every graph that for every natural number contains vertex-disjoint -minors contains infinitely many vertex-disjoint -minors. Andreae conjectured that every locally finite graph is ubiquitous. We give a disconnected counterexample to this conjecture. It remains open whether every connected locally finite graph is ubiquitous.
Keywords
Cite
@article{arxiv.2210.02711,
title = {On Andreae's Ubiquity Conjecture},
author = {Johannes Carmesin},
journal= {arXiv preprint arXiv:2210.02711},
year = {2022}
}