Clique-partitioned graphs

A graph \(G\) of order \(nv\) where \(n\geq 2\) and \(v\geq 2\) is said to be weakly \((n,v)\)-clique-partitioned if its vertex set can be decomposed in a unique way into \(n\) vertex-disjoint \(v\)-cliques. It is strongly \((n,v)\)-clique-partitioned if in addition, the only \(v\)-cliques of \(G\)...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Erskine, Grahame, Griggs, Terry, Širáň, Jozef
Format: Article
Language:English
Subjects:
Decomposition
Graphs
Online Access:Get full text
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Summary:A graph \(G\) of order \(nv\) where \(n\geq 2\) and \(v\geq 2\) is said to be weakly \((n,v)\)-clique-partitioned if its vertex set can be decomposed in a unique way into \(n\) vertex-disjoint \(v\)-cliques. It is strongly \((n,v)\)-clique-partitioned if in addition, the only \(v\)-cliques of \(G\) are the \(n\) cliques in the decomposition. We determine the structure of such graphs which have the largest possible number of edges.
ISSN:2331-8422
DOI:10.48550/arxiv.1809.00527