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Decomposable graphs and hypergraphs

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

S. L. Lauritzen ,
T. P. Speed  and
K. Vijayan
S. L. Lauritzen
Affiliation:
Institute for Elektronik Systems Aalborg UniversityBadehusvej 13 Aalborg, DK-9000, Denmark
T. P. Speed
Affiliation:
CSIRO Division of Mathematics and Statistics P.O. Box 1965, Canberra City ACT, 2601, Australia
K. Vijayan
Affiliation:
Department of Mathematics University of Western AustraliaNedlands, W.A. 6009, Australia
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Abstract

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We define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity.

Keywords

clique hypergraphstriangulated graphs.

MSC classification

Secondary: 05C65: Hypergraphs 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 12 - 29
Copyright
Copyright © Australian Mathematical Society 1984

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