Extension of hereditary classes with substitutions Original Research Article

Let G and H be graphs. A substitution of H in G instead of a vertex v∈V(G) is the graph G(v→H), which consists of disjoint union of H and G−v with the additional edge-set {xy: x∈V(H),y∈NG(v)}. For a hereditary class of graphs P, the substitutional closure of P is defined as the class P∗ consisting of all graphs which can be obtained from graphs in P by repeated substitutions. Let P be an arbitrary hereditary class for which a characterization in terms of forbidden induced subgraphs is known. We propose a method of constructing forbidden induced subgraphs for P∗.