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Algorithmica

, Volume 57, Issue 1, pp 74–81 | Cite as

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

  • Chính T. HoàngEmail author
  • Marcin Kamiński
  • Vadim Lozin
  • Joe Sawada
  • Xiao Shu
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.

Keywords

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

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Chính T. Hoàng
    • 1
    Email author
  • Marcin Kamiński
    • 2
  • Vadim Lozin
    • 3
  • Joe Sawada
    • 4
  • Xiao Shu
    • 4
  1. 1.Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.RUTCORRutgers UniversityPiscatawayUSA
  3. 3.DIMAP and Mathematics InstituteUniversity of WarwickCoventryUK
  4. 4.Computing and Information ScienceUniversity of GuelphGuelphCanada

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