Problem 533

Erdős Problem #533: declared status 'disproved'. Formalized: no. Let $\delta>0$. If $n$ is sufficiently large and $G$ is a graph on $n$ vertices with no $K_5$ and at least $\delta n^2$ edges then $G$ contains a set of $\gg_\delta n$ vertices containing no triangle. Prize: no. Tags: graph theory.