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Triangle-free subgraphs with large fractional chromatic number

Part of: Graph theory

Published online by Cambridge University Press:  29 June 2021

Bojan Mohar  and
Hehui Wu
Bojan Mohar*
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada
Hehui Wu
Affiliation:
Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China
*
*Corresponding author. Email: mohar@sfu.ca
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Abstract

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.

Keywords

chromatic numberfractional chromatic numberErdös–Hajnal conjecture

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 31 , Issue 1 , January 2022 , pp. 136 - 143
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

Supported in part by the NSERC Discovery Grant R611450 (Canada), by the Canada Research Chairs program, and by the Research Project J1-8130 of ARRS (Slovenia).

‡

Part of this work was done while the author was a PIMS Postdoctoral Fellow at the Department of Mathematics, Simon Fraser University, Burnaby, B.C.

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