Erdős Problem 1033

### What is the conjecture

https://www.erdosproblems.com/1033

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
$$h(n)\geq (2(\sqrt{3}-1)-o(1))n?$$

Status:open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading the linked Erdős Problems 1033 statement and inspecting existing formal conjectures in the repository for its conventions. Done means the conjecture is added as a Lean formalization with the stated definitions and bounds, but the issue does not identify a file or entry point.

Written by the indexing model from the issue text.