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Counterexamples to a conjecture of Harris on Hall ratio

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arxiv 1811.11116 v4 pith:O45WETSH submitted 2018-11-27 math.CO

Adam Blumenthal , Bernard Lidicky , Ryan R. Martin , Sergey Norin , Florian Pfender , Jan Volec This is my paper · ORCID
classification math.CO
keywords hallratiochromaticconjecturefractionalgraphharrisnumber
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abstract

The Hall ratio of a graph $G$ is the maximum value of $v(H) / \alpha(H)$ 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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