Every plane graph of maximum degree 8 has an edge-face 9-colouring

Ross J. Kang, Jean-Sébastien Sereni, Matěj Stehlík

Published 2009-12-24, updated 2011-03-08Version 2

An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\Delta\ge10$ can be edge-face coloured with $\Delta+1$ colours. Borodin's bound was recently extended to the case where $\Delta=9$. In this paper, we extend it to the case $\Delta=8$.