Deciding k-Colorability of P5-Free Graphs in Polynomial Time

The problem of computing the chromatic number of a P5-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 P5-free graph admits a k-coloring, and finding one, if it does.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Chính T. Hoàng, Marcin Kaminski, Vadim V. Lozin, Joe Sawada, Xiao Shu
• Keywords: ALGORITHMICA 2007, ALGORITHMICA 2010, Chromatic Number, P5-free Graph, Polynomial-time Algorithm