Erdős Problem 813

### What is the conjecture

https://www.erdosproblems.com/813

Let $h(n)$ be minimal such that every graph on $n$ vertices where every set of $7$ vertices contains a triangle (a copy of $K_3$) must contain a clique on at least $h(n)$ vertices. Estimate $h(n)$ - in particular, do there exist constants $c_1,c_2>0$ such that
$$n^{1/3+c_1}\ll h(n) \ll n^{1/2-c_2}?$$

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

The issue names no repository files, tests, or entry points; start by examining how existing conjectures are formalized in this Lean repository and identify related graph-theory entries. Done means adding Problem 813 as a formalized statement, but the issue does not specify the expected encoding or validation steps.

Written by the indexing model from the issue text.