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Triangle-free subgraphs with large fractional chromatic number
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Journal Article
Triangle-free subgraphs with large fractional chromatic number
2022
Overview
It is well known that for any integers k and g , there is a graph with chromatic number at least k and girth at least g . In 1960s, Erdös and Hajnal conjectured that for any k and g , there exists a number h ( k , g ), such that every graph with chromatic number at least h ( k , g ) contains a subgraph with chromatic number at least k and girth at least g . In 1977, Rödl proved the case when$g=4$, for arbitrary k . We prove the fractional chromatic number version of Rödl’s result.
Publisher
Cambridge University Press
Subject
