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.
CITATION STYLE
Dabrowski, K. K., Dross, F., Johnson, M., & Paulusma, D. (2016). Filling the complexity gaps for colouring planar and bounded degree graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9538, pp. 100–111). Springer Verlag. https://doi.org/10.1007/978-3-319-29516-9_9
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