Cyclic colorings of plane graphs with independent faces

Authors:
Jernej Azarija;Rok Erman;Daniel Král';Matja Krnc;Ladislav Stacho
Affiliations:
Department of Mathematics, University of Ljubljana, Jadranska19, 1111 Ljubljana, Slovenia;Department of Mathematics, University of Ljubljana, Jadranska19, 1111 Ljubljana, Slovenia;Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské námstí 25, 118 00 Prague 1, Czech Republic;Department of Mathematics, University of Ljubljana, Jadranska19, 1111 Ljubljana, Slovenia;Department of Mathematics, Simon Fraser University, 8888 University Dr, Burnaby, BC, V5A 1S6, Canada
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

Let G be a plane graph with maximum face size @D^*. If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with @D^*+1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors.