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arXiv · 1809.00527

Clique-partitioned graphs

Grahame Erskine·Terry Griggs·Jozef Širáň
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Abstract

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.

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Grahame Erskine, Terry Griggs, Jozef Širáň. 2022-04-01. Clique-partitioned graphs. https://doi.org/10.1016/j.dam.2022.02.024

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