Hard coloring problems in low degree planar bipartite graphs

Miroslav Chlebik; Janka Chlebikova

doi:10.1016/j.dam.2006.03.014

Hard coloring problems in low degree planar bipartite graphs

Miroslav Chlebik
, Janka Chlebikova

School of Computing

University of Sussex

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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.

Original language	English
Pages (from-to)	1960-1965
Journal	Discrete Applied Mathematics
Volume	154
Issue number	14
DOIs	https://doi.org/10.1016/j.dam.2006.03.014
Publication status	Published - 2006

Keywords

List Coloring
PreColoring
Planar graphs

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10.1016/j.dam.2006.03.014

1-s2.0-S0166218X06001260-main
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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.",

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PY - 2006

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N2 - 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.

AB - 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.

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KW - PreColoring

KW - Planar graphs

U2 - 10.1016/j.dam.2006.03.014

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VL - 154

SP - 1960

EP - 1965

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 14

ER -

Hard coloring problems in low degree planar bipartite graphs

Abstract

Keywords

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