Problem 500

Erdős Problem #500: declared status 'open'. Formalized: no. What is $\mathrm{ex}_3(n,K_4^3)$? That is, the largest number of $3$-edges which can placed on $n$ vertices so that there exists no $K_4^3$, a set of 4 vertices which is covered by all 4 possible $3$-edges. Current best: The current best upper bound is$$\mathrm{ex}_3(n,K_4^3)\leq 0.5611666\binom{n}{3},$$due to Razborov [Ra10]. Prize: $500. OEIS: A140462. Tags: graph theory, hypergraphs, turan number.