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Deciding k-colourability of $P_5$-free graphs in polynomial time

Chính T. Hoàng·Marcin Kamiński·Vadim Lozin·J. Sawada·X. Shu
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Abstract

The problem of computing the chromatic number of a $P_5$-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a $P_5$-free graph admits a $k$-colouring, for each fixed number of colours $k$, can be done in polynomial time. If such a colouring exists, our algorithm produces it.

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Chính T. Hoàng, Marcin Kamiński, Vadim Lozin, J. Sawada, X. Shu. 2007-02-07. Deciding k-colourability of $P_5$-free graphs in polynomial time. https://arxiv.org/abs/cs/0702043

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