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