DMGT

Discussiones Mathematicae Graph Theory 15(1) (1995) 11-18
DOI: https://doi.org/10.7151/dmgt.1002

REDUCIBLE PROPERTIES OF GRAPHS

P. Mihók and G. Semanišin

Department of Geometry and Algebra, Faculty of Sciences,
P. J. Šafárik's University
Jesenná 5, 04154 Košice, Slovak Republic

Abstract

Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈L, the reducible property R = P₁ºP₂ 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

1991 Mathematics Subject Classification: 05C15, 05C75

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