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Clique coverings of graphs V: maximal-clique partitions

Published online by Cambridge University Press:  17 April 2009

N.J. Pullman ,
H. Shank  and
W.D. Wallis
N.J. Pullman
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario K7L 3N6, Canada
H. Shank
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario K7L 3N6, Canada
W.D. Wallis
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia.
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Abstract

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A maximal-clique partition of a graph G is a way of covering G with maximal complete subgraphs, such that every edge belongs to exactly one of the subgraphs. If G has a maximal-clique partition, the maximal-clique partition number of G is the smallest cardinality of such partitions. In this paper the existence of maximal-clique partitions is discussed – for example, we explicitly describe all graphs with maximal degree at most four which have maximal-clique partitions - and discuss the maximal-clique partition number and its relationship to other clique covering and partition numbers. The number of different maximal-clique partitions of a given graph is also discussed. Several open problems are presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 3 , June 1982 , pp. 337 - 356
Copyright
Copyright © Australian Mathematical Society 1982

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