Question: [17] Let G = (V,E) with V = {1,...,n} be an undirected graph on n nodes with C(G|n, p) n(n1)/2, where p is a

[17] Let G = (V,E) with V = {1,...,n} be an undirected graph on n nodes with C(G|n, p) ≥ n(n−1)/2, where p is a fixed program to be used to reconstruct G. A clique of a graph is a complete subgraph of that graph. Show that G does not contain a clique on more than 1 +2 log n

nodes.

Comments. Hint: use Section 6.3.1.

To compare this result with a similar one about randomly generated graphs, N. Alon, J.H. Spencer, and P.

Erd˝os in [The Probabilistic Method, Wiley, 1992, pp. 86–87] show that a random graph with edge probability 1 2 contains a clique on 2 log n nodes with probability at least 1 − 1/en2

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