On the factorization of reducible properties of graphs into irreducible factors

A hereditary property R of graphs is said to be reducible if there exist hereditary properties P1,P2 such that G ∈ R if and only if the set of vertices of G can be partitioned into V (G) = V1 ∪ V2 so that 〈V1〉 ∈ P1 and 〈V2〉 ∈ P2. The problem of the factorization of reducible properties into irreducible factors is investigated.