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Reducible properties of graphs

P. Mihók;  G. Semanišin — 1995

Discussiones Mathematicae Graph Theory

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 ⟨ V ₁ ⟩ G ∈ P ₁ and ⟨ V ₂ ⟩ G ∈ P ₂ . 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.

On the factorization of reducible properties of graphs into irreducible factors

P. Mihók;  R. Vasky — 1995

Discussiones Mathematicae Graph Theory

A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.

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