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


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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Correspondence to Chính T. Hoàng.

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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).

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