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Coloring vertices of claw-free graphs in three colors

Author

Listed:
  • Vadim Lozin

    (The University of Warwick)

  • Christopher Purcell

    (The University of Warwick)

Abstract

We study the computational complexity of the vertex 3-colorability problem in the class of claw-free graphs. Both the problem and the class received much attention in the literature, separately of each other. However, very little is known about the 3-colorability problem restricted to the class of claw-free graphs beyond the fact the problem is NP-complete under this restriction. In this paper we first strengthen this negative fact by revealing various further restrictions under which the problem remains NP-complete. Then we derive a number of positive results that deal with polynomially solvable cases of the problem in the class of claw-free graphs.

Suggested Citation

  • Vadim Lozin & Christopher Purcell, 2014. "Coloring vertices of claw-free graphs in three colors," Journal of Combinatorial Optimization, Springer, vol. 28(2), pages 462-479, August.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:2:d:10.1007_s10878-012-9577-5
    DOI: 10.1007/s10878-012-9577-5
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    References listed on IDEAS

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    1. Xueliang Li & Wenan Zang, 2005. "A Combinatorial Algorithm for Minimum Weighted Colorings of Claw-Free Perfect Graphs," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 331-347, June.
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