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

@article{Hong2007DecidingKO,
  title={Deciding k-Colorability of P 5-Free Graphs in Polynomial Time},
  author={Ch{\'i}nh T. Ho{\`a}ng and Marcin Jakub Kaminski and Vadim V. Lozin and Joe Sawada and Xiao Shu},
  journal={Algorithmica},
  year={2007},
  volume={57},
  pages={74-81}
}
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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