An edge-face coloring of a plane graph with edge set $E$ and face set $F$ is a coloring of the elements of $E\cup F$ such that adjacent or incident elements receive different colors. Borodin proved that every plane graph of maximum degree $\Delta \ge 10$ can be edge-face colored with $\Delta + 1$ colors. Borodin’s bound was recently extended to the case where $\Delta = 9$. In this paper, we extend it to the case $\Delta = 8$.

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SIAM Journal on Discrete Mathematics

Kang, R., Sereni, J.-S., & Stehlík, M. (2011). Every plane graph of maximum degree 8 has an edge-face 9-colouring. SIAM Journal on Discrete Mathematics, 25(2), 514–533.