Geodesic
On the completeness of decomposable properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 229-236

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Let ₁,₂ be additive hereditary properties of graphs. A (₁,₂)-decomposition of a graph G is a partition of E(G) into sets E₁, E₂ such that induced subgraph G[E_i] has the property _i, i = 1,2. Let us define a property ₁⊕₂ by G: G has a (₁,₂)-decomposition.
Keywords: decomposition, hereditary property, completeness 
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Hałuszczak, Mariusz; Vateha, Pavol. On the completeness of decomposable properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 229-236. http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a8/