Geodesic
The decomposability of additive hereditary properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 281-291.

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If ₁,...,ₙ are properties of graphs, then a (₁,...,ₙ)-decomposition of a graph G is a partition E₁,...,Eₙ of E(G) such that G[E_i], the subgraph of G induced by E_i, is in _i, for i = 1,...,n. We define ₁ ⊕...⊕ ₙ as the property G ∈ : G has a (₁,...,ₙ)-decomposition. A property is said to be decomposable if there exist non-trivial hereditary properties ₁ and ₂ such that = ₁⊕ ₂. We study the decomposability of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ, ₖ, ₖ and ^p.
Keywords: property of graphs, additive, hereditary, decomposable property of graphs 
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Broere, Izak; Dorfling, Michael. The decomposability of additive hereditary properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 281-291. http://geodesic.mathdoc.fr/item/DMGT_2000_20_2_a11/

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