Abstract
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover numberscc(G) of a graph G, is defined as the smallest possible weight of a clique covering of G. Let Kt(d) denote the complete t-partite graph with each part of size d. We prove that for any fixed d≥2, we have limt→∞scc(Kt(d))=d2tlogt. This disproves a conjecture of Davoodi et al. (2016).
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