On the complexity of the selective graph coloring problem in some special classes of graphs

In this paper, we consider the selective graph coloring problem. Given an integer k ≥ 1 and a graph G = (V,E) with a partition V1, . . . , Vp of V , it consists in deciding whether there exists a set V ∗ in G such that ∣V ∗ ∩ Vi∣ = 1 for all i ∈ {1, . . . , p}, and such that the graph induced by V ∗ is k-colorable. We investigate the complexity status of… (More)