Erdős Problem 1075

### What is the conjecture

https://www.erdosproblems.com/1075

Let $r\geq 3$. There exists $c_r>r^{-r}$ such that, for any $\epsilon>0$, if $n$ is sufficiently large, the following holds.

Any $r$-uniform hypergraph on $n$ vertices with at least $(1+\epsilon)(n/r)^r$ many edges contains a subgraph on $m$ vertices with at least $c_rm^r$ edges, where $m=m(n)\to \infty$ as $n\to \infty$.

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

No file, test, or entry point is named. Read existing conjecture formalizations in the repository and use the linked Erdős Problems page as the statement source; done means adding a formal statement for Problem 1075.

Written by the indexing model from the issue text.