Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties

Abstract

An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let L a denote a class of all such properties. In the paper, we consider Hreducible over L a properties with H being a xed graph. The niteness of the sets of all minimal forbidden graphs is analyzed for such properties.