Minimal forbidden subgraphs of reducible graph properties
A property of graphs is any class of graphs closed under isomorphism. Let ₁,₂,...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable if the vertex set V(G) can be partitioned into n sets, V₁,V₂,..., Vₙ, such that for each i = 1,2,...,n, the graph . We write ₁∘₂∘...∘ₙ for the property of all graphs which have a (₁,₂,...,ₙ)-partition. An additive induced-hereditary property is called reducible if there exist additive induced-hereditary properties ₁ and ₂ such that = ₁∘₂. Otherwise...