We consider four combinatorial optimization problems (independent set, clique, coloring, partition into cliques) for a special graph class. These graphs G=(N,E) are generated by nondisjoint union of a cograph and a graph with m disjoint cliques. Such graphs can be described as transfer flow graphs. At first, we show that these graphs occur as compatibility graphs in the synthesis of hardware configurations. Then we prove that the clique problem can be solved in O(¦N¦2) steps and that the other problems are NP-complete. Moreover, all four problems can be solved in polynomial time if m is constant.
