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Triangle-free subgraphs with large fractional chromatic number
- Part of
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- Journal:
- Combinatorics, Probability and Computing / Volume 31 / Issue 1 / January 2022
- Published online by Cambridge University Press:
- 29 June 2021, pp. 136-143
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- Article
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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.
