Vertex-critical graphs far from edge-criticality
Year: 2024
Type: article
Abstract: Let $r$ be any positive integer. We prove that for every sufficiently large $k$ there exists a $k$ -chromatic vertex-critical graph $G$ such that $\chi (G-R)=k$ for every set $R \subseteq E(G)$ with $|R|\le r$ . This partially solves a problem posed by Erdős in 1985, who asked whether the above statement holds for $k \ge 4$ .
Authors: Anders Martinsson, Raphael Steiner
Institutions: ETH Zurich, Institute of Theoretical Computer Science
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4403341511