Erdős Problem 1075

[mo271]

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
• This issue is up for grabs: I would like to see this conjecture added by somebody else