Geodesic
Reducible properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 11-18

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Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that 〈V₁〉_G ∈ P₁ and 〈V₂〉_G ∈ P₂. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.
Keywords: hereditary property of graphs, additivity, reducibility 
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Mihók, P.; Semanišin, G. Reducible properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 11-18. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a1/