Deciding k-colourability of P5-free graphs in polynomial time
Abstract
The problem of computing the chromatic number of a P5-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a P5-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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