Erdős Problems

OPEN

Is it true that \[\mathrm{ex}(n; K_{r,r}) \gg n^{2-1/r}?\]

Kövári, Sós, and Turán [KST54] proved \[\mathrm{ex}(n; K_{r,r}) \ll n^{2-1/r}.\] Brown [Br66] proved the conjectured lower bound when $r=3$.