| Abstract: | A 1992 conjecture of Alon and Spencer says, roughly, that the ordinary random graph Gn,1/2 typically admits a covering of a constant fraction of its edges by edge‐disjoint, nearly maximum cliques. We show that this is not the case. The disproof is based on some (partial) understanding of a more basic question: for  and A1,…,At chosen uniformly and independently from the k‐subsets of {1,…,n}, what can one say about  Our main concern is trying to understand how closely the answers to this and a related question about matchings follow heuristics gotten by pretending that certain (dependent) choices are made independently. |
