Problem 712

Erdős Problem #712: declared status 'open'. Formalized: no. Determine, for any $k>r>2$, the value of$$\frac{\mathrm{ex}_r(n,K_k^r)}{\binom{n}{r}},$$where $\mathrm{ex}_r(n,K_k^r)$ is the largest number of $r$-edges which can placed on $n$ vertices so that there exists no set of $k$ vertices which is covered by all $\binom{k}{r}$ possible $r$-edges. Prize: $500. Tags: graph theory, hypergraphs, turan number.