List-edge-colouring planar graphs with precoloured edges

Abstract

Let $G$ be a simple planar graph of maximum degree $\Delta$, let $t$ be a positive integer, and let $L$ be an edge list assignment on $G$ with $|L(e)|\ge \Delta +t$ 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 $d\le t$ and either $d\le t-4$ or $\Delta$ is large enough ($\Delta \ge 16+d$ suffices). If $d>t$, there are examples for any choice of $\Delta$ where the extension is impossible.

14 pages, 3 figures, 1 table