Filling the Complexity Gaps for Colouring Planar and Bounded Degree Graphs

  • Konrad K. Dabrowski
  • François Dross
  • Matthew Johnson
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9538)


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.


List colouring Choosability Planar graphs Maximum degree 



We thank Steven Kelk for helpful comments on an earlier version of this paper.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Konrad K. Dabrowski
    • 1
  • François Dross
    • 2
    • 3
  • Matthew Johnson
    • 1
  • Daniël Paulusma
    • 1
  1. 1.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  2. 2.Ecole Normale Supérieure de LyonLyonFrance
  3. 3.Laboratoire d’Informatique, de Robotique et de Microélectronique de MontpellierMontpellierFrance

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