Polynomial-time algorithms for minimum weighted colorings of (P5,P¯5)-free graphs and similar graph classes

We design an O(n3)O(n3) algorithm to find a minimum weighted coloring of a (P5,P¯5)-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.