Article ID Journal Published Year Pages File Type
4651958 Electronic Notes in Discrete Mathematics 2015 6 Pages PDF
Abstract

It is well known that for any k and g, there is a graph with chromatic number at least k and girth at least g. In 1970's, Erdős and Hajnal conjectured that for any numbers k and g, there exists a number f(k,g), such that every graph with chromatic number at least f(k, g) contains a subgraph with chromatic number at least k and girth at least g. In 1978, Rödl proved the case for g=4 and arbitrary k. We prove the fractional chromatic number version of Rödl's result.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics