OPENHARDgraph theoryextremal graph theory
Does every graph on $n$ vertices with $>\mathrm{ex}(n;C_4)$ edges contain $\gg n^{1/2}$ many copies of $C_4$?
Notes: Erdos and Simonovits could not even prove that at least 2 copies are guaranteed. He, Ma, and Yang proved the conjecture when n = q^2+q+1 for even q.
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