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The decomposability of additive hereditary properties of graphs
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If β,...,β are properties of graphs, then a (β,...,β)-decomposition of a graph G is a partition Eβ,...,Eβ of E(G) such that , the subgraph of G induced by , is in , for i = 1,...,n. We define β β...β β as the property {G β : G has a (β,...,β)-decomposition}. A property is said to be decomposable if there exist non-trivial hereditary properties β and β such that = ββ β. We study the decomposability of the well-known properties of graphs β, β, β, β, β, β and