Extension of hereditary classes with substitutions

Abstract

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∈N G(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 ∗ .