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International Workshop on Combinatorial Algorithms

IWOCA 2015: Combinatorial Algorithms pp 124–135Cite as

List Colouring and Partial List Colouring of Graphs On-line

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9538))

Abstract

In this paper, we investigate the problem of graph list colouring in the on-line setting. We provide several results on paintability of graphs in the model introduced by Schauz [18] and Zhu [25]. We prove that the on-line version of Ohba’s conjecture is true for the class of planar graphs. We show that the conjecture for partial list colouring on-line holds for several graph classes, namely claw-free graphs, maximal planar graphs, series-parallel graphs, and chordal graphs.

M. Derka—The first author was supported by Vanier CGS.

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Notes

  1. 1.

    Ohba’s conjecture was proved by Noel, Reed and Wu [16] in 2014.

  2. 2.

    Note that \(K_{0,4}\) is not connected, so it is both 1-chromatic and 1-paintable.

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Author information

Authors and Affiliations

  1. D. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Martin Derka, Alejandro López-Ortiz & Daniela Maftuleac

Authors
  1. Martin Derka
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  2. Alejandro López-Ortiz
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  3. Daniela Maftuleac
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Corresponding author

Correspondence to Martin Derka .

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Verona, Verona, Italy

    Zsuzsanna Lipták

  2. Dept. of Computing and Software, McMaster University, Hamilton, Canada

    William F. Smyth

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Derka, M., López-Ortiz, A., Maftuleac, D. (2016). List Colouring and Partial List Colouring of Graphs On-line. 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_11

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  • DOI: https://doi.org/10.1007/978-3-319-29516-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29515-2

  • Online ISBN: 978-3-319-29516-9

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