A note on 2-facial coloring of plane graphs

Authors:
Mickaël Montassier;André Raspaud
Affiliations:
LaBRI UMR CNRS 5800, Université Bordeaux I, 33405 Talence Cedex, France;LaBRI UMR CNRS 5800, Université Bordeaux I, 33405 Talence Cedex, France
Venue:
Information Processing Letters
Year:
2006

Citing 4
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Abstract

An l-facial coloring of a plane graph is a vertex coloring such that any two different vertices joined by a facial walk of length at most l receive distinct colors. It is known that every plane graph admits a 2-facial coloring using 8 colors [D. Kral, T. Madaras, R. Skrekovski, Cyclic, diagonal and facial coloring, European J. Combin. 3-4 (26) (2005) 473-490]. We improve this bound for plane graphs with large girth and prove that if G is a plane graph with girth g=14 (resp. 10, 8) then G admits a 2-facial coloring using 5 colors (resp. 6, 7). Moreover, we give exact bounds for outerplanar graphs and K"4-minor free graphs.