Year: 2025
Type: article
Abstract: In 1992, Erdős and Hajnal posed the following natural problem: Does there exist, for every , an integer such that every graph with chromatic number at least contains edge‐disjoint cycles on the same vertex set? We solve this problem in a strong form, by showing that there exist ‐vertex graphs with fractional chromatic number that do not even contain a 4‐regular subgraph. This implies that no such number exists for . We show that, assuming a conjecture of Harris, the bound on the fractional chromatic number in our result cannot be improved. (After our paper was written, Harris' conjecture was proved by Martinsson.)
DOI: 10.1112/blms.70262
Authors: Barnabás Janzer, Raphael Steiner, Benny Sudakov
Institutions: ETH Zurich, Institute for Operations Research
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
OpenAlex ID: W7115771482