Covering the edges of a random graph by cliques

Abstract

The clique cover number θ1(G) of a graph G is the minimum number of cliques required to cover the edges of graph G. In this paper we consider θ1(Gn,p), for p constant. (Recall that in the random graph Gn,p, each of the ( n 2 ) edges occurs independently with probability p). Bollobas, Erdős, Spencer and West [1] proved that whp (i.e. with probability 1-o(1) as n→∞) (1− o(1))n 4(log2 n) 2 ≤ θ1(Gn,.5) ≤ cn ln lnn (lnn)2 .