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Coupled choosability of plane graphs

✍ Scribed by Weifan Wang; Ko-Wei Lih

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 197 KB
Volume: 58
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20292

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✦ Synopsis

Abstract

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

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