Problem 1033

Erdős Problem #1033: declared status 'open'. Formalized: no. Let $h(n)$ be such that every graph on $n$ vertices with $>n^2/4$ many edges contains a triangle whose vertices have degrees summing to at least $h(n)$. Estimate $h(n)$. In particular, is it true that$$h(n)\geq (2(\sqrt{3}-1)-o(1))n?$$ Current best: The lower bound was improved to $\frac{21}{16}n$ by Fan [Fa88]. Prize: no. Tags: graph theory.