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arXiv · 1709.04027

List-edge-colouring planar graphs with precoloured edges

Joshua Harrelson·Jessica McDonald·Gregory J. Puleo
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Abstract

Let $G$ be a simple planar graph of maximum degree $Δ$, let $t$ be a positive integer, and let $L$ be an edge list assignment on $G$ with $|L(e)| \geq Δ+t$ for all $e \in E(G)$. We prove that if $H$ is a subgraph of $G$ that has been $L$-edge-coloured, then the edge-precolouring can be extended to an $L$-edge-colouring of $G$, provided that $H$ has maximum degree $d\leq t$ and either $d \leq t-4$ or $Δ$ is large enough ($Δ\geq 16+d$ suffices). If $d>t$, there are examples for any choice of $Δ$ where the extension is impossible.

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Joshua Harrelson, Jessica McDonald, Gregory J. Puleo. 2018-07-09. List-edge-colouring planar graphs with precoloured edges. https://arxiv.org/abs/1709.04027

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