Erdős Problem 1013

### What is the conjecture

https://www.erdosproblems.com/1013

Let $h_3(k)$ be the minimal $n$ such that there exists a triangle-free graph on $n$ vertices with chromatic number $k$. Find an asymptotic for $h_3(k)$, and also prove
$$\lim_{k\to \infty}\frac{h_3(k+1)}{h_3(k)}=1.$$

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