The entire choosability of plane graphs
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A plane graph \(G\) is entirely \(k\)-choosable if, for every list \(L\) of colors satisfying \(L(x)=k\) for all \(x\in V(G)\cup E(G) \cup F(G)\), there exists a coloring which assigns to each vertex, each edge and each face a color from its list so that any adjacent or incident elements receive different colors. In 1993, Borodin proved that every plane graph \(G\) with maximum degree \(\Delta \ge 12\) is entirely \((\Delta +2)\)-choosable. In this paper, we improve this result by replacing 12 by 10.
KeywordsPlane graph Entire choosability Maximum degree
The authors would like to thank the referees for their valuable comments that helped to improve this work. Weifan Wang: Research supported by NSFC (No. 11371328). Yiqiao Wang: Research supported by NSFC (No. 11301035)