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.
First and last author supported by EPSRC (EP/K025090/1).
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Acknowledgements
We thank Steven Kelk for helpful comments on an earlier version of this paper.
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Dabrowski, K.K., Dross, F., Johnson, M., Paulusma, D. (2016). Filling the Complexity Gaps for Colouring Planar and Bounded Degree Graphs. In: Lipták, Z., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2015. Lecture Notes in Computer Science(), vol 9538. Springer, Cham. https://doi.org/10.1007/978-3-319-29516-9_9
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