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arXiv · 2002.10109

The edge colorings of $K_{5}$-minor free graphs

Jieru Feng·Yuping Gao·Jianliang Wu
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Abstract

In 1965, Vizing proved that every planar graph $G$ with maximum degree $Δ\geq 8$ is edge $Δ$-colorable. It is also proved that every planar graph $G$ with maximum degree $Δ=7$ is edge $Δ$-colorable by Sanders and Zhao, independently by Zhang. In this paper, we extend the above results by showing that every $K_5$-minor free graph with maximum degree $Δ$ at least seven is edge $Δ$-colorable.

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Jieru Feng, Yuping Gao, Jianliang Wu. 2020-02-24. The edge colorings of $K_{5}$-minor free graphs. https://arxiv.org/abs/2002.10109

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