Erdős Problem #1079

The problem

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?

Statement quoted from erdosproblems.com/1079, maintained by Thomas Bloom. Original source: [Er75]. Current status there: solved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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