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arXiv · 2109.11447

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

Eckhard Steffen·Isaak H. Wolf
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Abstract

A finite simple connected graph $G$ with maximum degree $k$ is $k$-critical if it has chromatic index $χ'(G)=k+1$ and $χ'(G-e)=k$ 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.

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Eckhard Steffen, Isaak H. Wolf. 2022-05-31. Even factors in edge-chromatic-critical graphs with a small number of divalent vertices. https://doi.org/10.1007/s00373-022-02506-x

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