Even factors in edge-chromatic-critical graphs with a small number of divalent vertices

Abstract

A finite simple connected graph $G$ with maximum degree $k$ is $k$-critical if it has chromatic index ${\chi }^{\prime }(G)=k+1$ and ${\chi }^{\prime }(G-e)=k$ for every edge $e\in E(G)$. Bej and the first author raised the question whether every $k$-critical graph has an even factor. We prove that every $k$-critical graph with at most $2k-6$ vertices of degree 2 has an even factor.

arXiv comment11 pages

References in corpus (1)

• Fractional matchings, component-factors and edge-chromatic critical graphs