@MISC{Zverovich01extensionof, author = {Igor Zverovich}, title = {Extension of Hereditary Classes With Substitutions}, year = {2001} }

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Abstract

Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G \Gamma v with the additional edge-set fxy : x 2 V (H); y 2 NG (v)g. 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 . RRR 14-2001 Page 1 1