Clique-partitioned graphs

Erskine, Grahame; Griggs, Terry and Širáň, Jozef (2022). Clique-partitioned graphs. Discrete Applied Mathematics, 314 pp. 238–248.

DOI: https://doi.org/10.1016/j.dam.2022.02.024

Abstract

A graph G of order nv where n ≥ 2 and v ≥ 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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