We know that for general graphs vertex coloring problem/ minimum clique cover problem are NP-hard and for perfect graphs, they can be solved in polynomial time. There are classes of graphs which are perfect, e.g., bipartite graphs, chordal graphs, linear graphs, etc.
My question is that:
Are there any families of graphs that we know for them vertex coloring problem/ minimum clique cover problem are NP-hard? I appreciate if someone can give the name of some of them or any reference for them (in case they exist).
I have a problem and I want to show that it is hard and I want to find such a family of graphs and use them as an instance for my problem.