Counterexamples to a Conjecture of Harris on Hall Ratio
نویسندگان
چکیده
The Hall ratio of a graph $G$ is the maximum value $v(H) / \alpha(H)$ taken over all non-null subgraphs $H$ $G$. For any graph, lower-bound on its fractional chromatic number. In this note, we present various constructions graphs whose number grows much faster than their ratio. This refutes conjecture Harris.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2022
ISSN: ['1095-7146', '0895-4801']
DOI: https://doi.org/10.1137/18m1229420