Problem 1021

Erdős Problem #1021: declared status 'proved'. Formalized: no. Is it true that, for every $k\geq 3$, there is a constant $c_k>0$ such that$$\mathrm{ex}(n,G_k) \ll n^{3/2-c_k},$$where $G_k$ is the bipartite graph between $\{y_1,\ldots,y_k\}$ and $\{z_1,\ldots,z_{\binom{k}{2}}\}$, with each $z_j$ joined to a unique pair of $y_i$? Prize: no. Tags: graph theory.