Finding cliques using few probes

Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from Gn,12 (and hence is likely to have a clique of size roughly 2logn), then for every delta l, there is an alpha<2 (that may depend on delta and l) such that no algorithm that makes n(delta) probes in l rounds is likely (over the choice of the random graph) to output a clique of size larger than alpha logn.