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arXiv · 0912.4770

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

Ross J. Kang·Jean-Sébastien Sereni·Matěj Stehlík
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Abstract

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 $Δ\ge10$ can be edge-face coloured with $Δ+1$ colours. Borodin's bound was recently extended to the case where $Δ=9$. In this paper, we extend it to the case $Δ=8$.

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Ross J. Kang, Jean-Sébastien Sereni, Matěj Stehlík. 2011-03-08. Every plane graph of maximum degree 8 has an edge-face 9-colouring. https://doi.org/10.1137/090781206

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