Counterexamples to a conjecture of Harris on Hall ratio
Combinatorics
2020-04-27 v4
Abstract
The Hall ratio of a graph is the maximum value of taken over all non-null subgraphs of . For any graph, the Hall ratio is a lower-bound on its fractional chromatic number. In this note, we present various constructions of graphs whose fractional chromatic number grows much faster than their Hall ratio. This refutes a conjecture of Harris.
Cite
@article{arxiv.1811.11116,
title = {Counterexamples to a conjecture of Harris on Hall ratio},
author = {Adam Blumenthal and Bernard Lidicky and Ryan R. Martin and Sergey Norin and Florian Pfender and Jan Volec},
journal= {arXiv preprint arXiv:1811.11116},
year = {2020}
}