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arXiv · 1811.11116

Counterexamples to a conjecture of Harris on Hall ratio

Adam Blumenthal·Bernard Lidicky·Ryan R. Martin·Sergey Norin·Florian Pfender·Jan Volec
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Abstract

The Hall ratio of a graph $G$ is the maximum value of $v(H) / α(H)$ taken over all non-null subgraphs $H$ of $G$. 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.

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Adam Blumenthal, Bernard Lidicky, Ryan R. Martin, Sergey Norin, Florian Pfender, Jan Volec. 2020-04-24. Counterexamples to a conjecture of Harris on Hall ratio. https://arxiv.org/abs/1811.11116

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