Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646600 | Discrete Mathematics | 2016 | 12 Pages |
Abstract
A plane graph GG is entirely kk-choosable if, for every list LL of colors satisfying L(x)=kL(x)=k for all x∈V(G)∪E(G)∪F(G)x∈V(G)∪E(G)∪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. It was known that every plane graph GG with maximum degree Δ≥10Δ≥10 is entirely (Δ+2)(Δ+2)-choosable. In this paper, we improve this result by showing that every plane graph GG with Δ=9Δ=9 is entirely 11-choosable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Xiaoxue Hu, Weifan Wang, Wai Chee Shiu, Yiqiao Wang,