  In 1976 Erdos, Kleitman and Rothschild determined the number of graphs
without a clique of size $\ell$. In this note we extend their result to the
case of forbidden cliques of increasing size. More precisely we prove that for
$\ell_n \le \frac12(\log n)^{1/4}$ there are
$$2^{(1-1/(\ell_n-1))n^2/2+o(n^2/\ell_n)}$$ $K_{\ell_n}$-free graphs of order
$n$. Our proof is based on the recent hypergraph container theorems of Saxton,
Thomason and Balogh, Morris, Samotij, in combination with a theorem of Lovasz
and Simonovits.
