List edge-colouring and total colouring in graphs of low treewidth

Abstract

We prove that the list chromatic index of a graph of maximum degree $\Delta$ and treewidth $\le \sqrt{2\Delta }-3$ is $\Delta$; and that the total chromatic number of a graph of maximum degree $\Delta$ and treewidth $\le \Delta /3+1$ is $\Delta +1$. This improves results by Meeks and Scott.

arXiv comment10 pages