DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 20(2) (2000) 281-291
DOI: 10.7151/dmgt.1127

THE DECOMPOSABILITY OF ADDITIVE HEREDITARY PROPERTIES OF GRAPHS

Izak Broere and Michael J. Dorfling

Department of Mathematics
Faculty of Science, Rand Afrikaans University
P.O. Box 524, Auckland Park, 2006 South Africa

e-mail: ib@na.rau.ac.za

Abstract

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1,…,Pn are properties of graphs, then a (P1, …, Pn)-decomposition of a graph G is a partition E1, …, En of E(G) such that G[Ei], the subgraph of G induced by Ei, is in Pi, for i = 1, …, n. We define P1 ⊕…⊕Pn as the property { G ∈ ℑ: G has a (P1, …, Pn)−decomposition }. A property P is said to be decomposable if there exist non-trivial hereditary properties P1 and P2 such that P = P1P2. We study the decomposability of the well-known properties of graphs ℑk, Ok, Wk, Tk, Sk, Dk and O p.

Keywords: property of graphs, additive, hereditary, decomposable property of graphs.

2000 Mathematics Subject Classification: O5C70.

References

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Received 5 September 2000
Revised 13 November 2000