Hard coloring problems in low degree planar bipartite graphs

Authors:
Miroslav Chlebík;Janka Chlebíková
Affiliations:
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany;Department of Informatics Educations, Faculty of Mathematics, Physics and Informatics, Mlynská dolina, Bratislava, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

In this paper we prove that the PRECOLORING EXTENSION problem on graphs of maximum degree 3 is polynomially solvable, but even its restricted version with 3 colors is NP-complete on planar bipartite graphs of maximum degree 4.The restricted version of LIST COLORING, in which the union of all lists consists of 3 colors, is shown to be NP-complete on planar 3-regular bipartite graphs.