Entire colouring of plane graphs
Journal of Combinatorial Theory Series B
Note: A note on entire choosability of plane graphs
Discrete Applied Mathematics
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A plane graph G is coupled k-choosable if, for any list assignment L satisfying $|{{L}}({{x}})|= {{k}}$ for every ${{x}}\in {{V}}({{G}})\cup {{F}}({{G}})$, there is a coloring that assigns to each vertex and each face a color from its list such that any two adjacent or incident elements receive distinct colors. We prove that every plane graph is coupled 7-choosable. We further show that maximal plane graphs, ${{K}}_{{4}}$-minor free graphs, and plane graphs with maximum degree at most three are coupled 6-choosable. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 27–44, 2008