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Deciding k-Colorability of P 5-Free Graphs in Polynomial Time

Algorithmica volume 57, pages 74–81 (2010)Cite this article

Abstract

The problem of computing the chromatic number of a P 5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixed integer k, there exists a polynomial-time algorithm determining whether or not a P 5-free graph admits a k-coloring, and finding one, if it does.

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Authors and Affiliations

  1. Physics and Computer Science, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, N2L 3C5, Canada

    Chính T. Hoàng

  2. RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ, 08854, USA

    Marcin Kamiński

  3. DIMAP and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Vadim Lozin

  4. Computing and Information Science, University of Guelph, Guelph, Canada

    Joe Sawada & Xiao Shu

Authors
  1. Chính T. Hoàng
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  2. Marcin Kamiński
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  3. Vadim Lozin
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  4. Joe Sawada
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  5. Xiao Shu
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Corresponding author

Correspondence to Chính T. Hoàng.

Additional information

C.T. Hoàng’s and J. Sawada’s research supported by NSERC.

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Hoàng, C.T., Kamiński, M., Lozin, V. et al. Deciding k-Colorability of P 5-Free Graphs in Polynomial Time. Algorithmica 57, 74–81 (2010). https://doi.org/10.1007/s00453-008-9197-8

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  • DOI: https://doi.org/10.1007/s00453-008-9197-8

Keywords

  • Graph coloring
  • Dominating clique
  • Polynomial-time algorithm
  • P5-free graph