Filling the Complexity Gaps for Colouring Planar and Bounded Degree Graphs

Konrad K Dabrowski,François Dross,Matthew Johnson,Daniël Paulusma

doi:10.1007/978-3-319-29516-9_9

Filling the Complexity Gaps for Colouring Planar and Bounded Degree Graphs

Konrad K Dabrowski, François Dross + Show 2 more

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https://doi.org/10.1007/978-3-319-29516-9_9

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Publication Date: Jan 1, 2016
Citations: 17	License type: cc-by

Affiliation: Durham University, École Normale Supérieure de Lyon, Montpellier Laboratory of Informatics, Robotics and Microelectronics

#List Colouring #Planar Triangle-free Graphs + Show 8 more

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Abstract

We consider a natural restriction of the List Colouring problem, k-Regular List Colouring, which corresponds to the List Colouring problem where every list has size exactly k. We give a complete classification of the complexity of k-Regular List Colouring restricted to planar graphs, planar bipartite graphs, planar triangle-free graphs and to planar graphs with no 4-cycles and no 5-cycles. We also give a complete classification of the complexity of this problem and a number of related colouring problems for graphs with bounded maximum degree.

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