What is the conjecture

https://www.erdosproblems.com/1079

Let $r\geq 4$. If $G$ is a graph on $n$ vertices with at least $\mathrm{ex}(n;K_r)$ edges then must $G$ contain a vertex with degree $d\gg_r n$ whose neighbourhood contains at least $\mathrm{ex}(d;K_{r-1})$ edges?

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else