On hereditary properties of composition graphs
The composition graph of a family of n+1 disjoint graphs is the graph H obtained by substituting the n vertices of H₀ respectively by the graphs H₁,H₂,...,Hₙ. If H has some hereditary property P, then necessarily all its factors enjoy the same property. For some sort of graphs it is sufficient that all factors have a certain common P to endow H with this P. For instance, it is known that the composition graph of a family of perfect graphs is also a perfect graph (B. Bollobas, 1978), and the...