We provide a certifying algorithm for the problem of deciding whether a P5- free graph is 3-colorable by showing there are exactly six finite graphs that are P5-free and not 3-colorable and minimal with respect to this property.
@article{arxiv.0907.3497,
title = {A certifying algorithm for 3-colorability of P5-free graphs},
author = {Daniel Bruce and Chinh T. Hoang and Joe Sawada},
journal= {arXiv preprint arXiv:0907.3497},
year = {2009}
}