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Narrowing Down the Gap on the Complexity of Coloring Pk-Free Graphs

  • Hajo Broersma
  • Petr A. Golovach
  • Daniël Paulusma
  • Jian Song
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

A graph is P k -free if it does not contain an induced subgraph isomorphic to a path on k vertices. We show that deciding whether a P 8-free graph can be colored with at most four colors is an NP-complete problem. This improves a result of Le, Randerath, and Schiermeyer, who showed that 4-coloring is NP-complete for P 9-free graphs, and a result of Woeginger and Sgall, who showed that 5-coloring is NP-complete for P 8-free graphs. Additionally, we prove that the pre-coloring extension version of 4-coloring is NP-complete for P 7-free graphs, but that the pre-coloring extension version of 3-coloring is polynomially solvable for (P 2 + P 4)-free graphs, a subclass of P 7-free graphs.

Keywords

Polynomial Time Chromatic Number Truth Assignment Free Graph Thick Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hajo Broersma
    • 1
  • Petr A. Golovach
    • 1
  • Daniël Paulusma
    • 1
  • Jian Song
    • 1
  1. 1.School of Engineering and Computing Sciences, Science LaboratoriesDurham UniversityDurhamUK

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