Abstract :
In this paper we investigate the closure F∗ under substitution-composition of a family of graphs F, defined by a set L of forbidden configurations. We first prove that F∗ can be defined by a set L∗ of forbidden subgraphs. Next, using a counterexample we show that L∗ is not necessarily a finite set, even when L is finite. We then give a sufficient condition for L∗ to be finite and a simple algorithm for enumerating all the graphs of L∗. As application, we obtain new classes of perfect graphs.
