We design an O(n3) algorithm to find a minimum weighted coloring of a (P5,Pˉ5)-free graph. Furthermore, the same technique can be used to solve the same problem for several classes of graphs, defined by forbidden induced subgraphs, such as (diamond, co-diamond)-free graphs.
@article{arxiv.1409.0893,
title = {Polynomial-time algorithms for minimum weighted colorings of ($P_5, \bar{P}_5$)-free graphs and related graph classes},
author = {Chính T. Hoàng and D. Adam Lazzarato},
journal= {arXiv preprint arXiv:1409.0893},
year = {2014}
}