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ArticleOriginal scientific text

Title

On hereditary properties of composition graphs

Authors 1, 1

Affiliations

  1. Department of Computer Systems, Center for Technological Education, Affiliated with Tel-Aviv University, 52 Golomb St., P.O. Box 305, Holon 58102, Israel

Abstract

The composition graph of a family of n+1 disjoint graphs {Hi:0≤i≤n} is the graph H obtained by substituting the n vertices of H₀ respectively by the graphs H₁,H₂,...,Hₙ. If H has some hereditary property P, then necessarily all its factors enjoy the same property. For some sort of graphs it is sufficient that all factors {Hi:0≤i≤n} have a certain common P to endow H with this P. For instance, it is known that the composition graph of a family of perfect graphs is also a perfect graph (B. Bollobas, 1978), and the composition graph of a family of comparability graphs is a comparability graph as well (M.C. Golumbic, 1980). In this paper we show that the composition graph of a family of co-graphs (i.e., P₄-free graphs), is also a co-graph, whereas for θ₁-perfect graphs (i.e., P₄-free and C₄-free graphs) and for threshold graphs (i.e., P₄-free, C₄-free and 2K₂-free graphs), the corresponding factors {Hi:0≤i≤n} have to be equipped with some special structure.

Keywords

ENG
composition graph, co-graphs, θ₁-perfect graphs, threshold graphs

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Discussiones Mathematicae Graph Theory
1998/18/2
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Pages:
183-195
Main language of publication
English
Received
1997-10-21
Accepted
1998-05-04
Published
1998

DOI: 10.7151/dmgt.1074

Exact and natural sciences