A property of graphs is a non-empty set of graphs. A property P is called hereditary if every subgraph of any graph with property P also has property P. Let P1, . . . ,Pn be properties of graphs. We say that a graph G has property P1◦ · · · ◦Pn if the vertex set of G can be partitioned into n sets V1, . . . , Vn such that the subgraph of G induced by Vi has property Pi; i = 1, . . . , n. A here...
