Erdős Problem 644

### What is the conjecture

https://www.erdosproblems.com/644

Let $f(k,r)$ be minimal such that if $A_1,A_2,\ldots$ is a family of sets, all of size $k$, such that for every collection of $r$ of the $A_is$ there is some pair $\\{x,y\\}$ which intersects all of the $A_j$, then there is some set of size $f(k,r)$ which intersects all of the sets $A_i$. Is it true that
$$f(k,7)=(1+o(1))\frac{3}{4}k?$$
Is it true that for any $r\geq 3$ there exists some constant $c_r$ such that
$$f(k,r)=(1+o(1))c_rk?$$

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