ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 19(2) (1999) 229-236
DOI: 10.7151/dmgt.1097


Mariusz Hałuszczak

Institute of Mathematics
Technical University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: M.Hał

Pavol Vateha

Department of Geometry and Algebra
Faculty of Science, P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovak Republic


Let P1, P2 be additive hereditary properties of graphs. A (P1, P2)-decomposition of a graph G is a partition of E(G) into sets E1, E2 such that induced subgraph G[Ei] has the property Pi, i = 1,2. Let us define a property P1P2 by {G: G has a (P1,P2)-decomposition}.

A property D is said to be decomposable if there exists nontrivial additive hereditary properties P1, P2 such that D = P1P2. In this paper we determine the completeness of some decomposable properties and we characterize the decomposable properties of completeness 2.

Keywords: decomposition, hereditary property, completeness.

1991 Mathematics Subject Classification: 05C55, 05C70.


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Received 12 February 1999
Revised 20 October 1999