Regular clique covers of graphs

Archdeacon, A.; Froncek, D.; Jajcay, R.; Ryjacek, Z. and Siran, J. (2003). Regular clique covers of graphs. Australasian Journal of Combinatorics, 27(1) pp. 307–316.



A family of cliques in a graph G is said to be p-regular if any two cliquesin the family intersect in exactly p vertices. A graph G is said to have ap-regular k-clique cover if there is a p-regular family H of k-cliques of Gsuch that each edge of G belongs to a clique in H. Such a p-regular k-clique cover is separable if the complete subgraphs of order p that arise asintersections of pairs of distinct cliques of H are mutually vertex-disjoint.For any given integers p,k,l; p < k, we present bounds on the smallestorder of a graph that has a p-regular k-clique cover with exactly l cliques,and we describe all graphs that have p-regular separable k-clique coverswith l cliques.

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