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Counterexamples to a conjecture of Harris on Hall ratio

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 نشر من قبل Jan Volec
 تاريخ النشر 2018
  مجال البحث
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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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