Extension of hereditary classes with substitutions
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 . For a hereditary class of graphs , the substitutional closure of is defined as the class consisting of all graphs which can be obtained from graphs in by repeated substitutions. Let 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 .
hereditary class of graphs substitutional closure homogeneous set stability number