Every Plane Graph of Maximum Degree 8 has an Edge-Face 9-Coloring

Ross J. Kang, Jean-Sébastien Sereni, Matěj Stehlík
2011 SIAM Journal on Discrete Mathematics  
An edge-face colouring of a plane graph with edge set E and face set F is a colouring of the elements of E ∪ F such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree Δ>10 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.
doi:10.1137/090781206 fatcat:e63m7o5kbbhdhf47wt3myusly4