Erdős Problem 627

### What is the conjecture

https://www.erdosproblems.com/627

Let $\omega(G)$ denote the clique number of $G$ and $\chi(G)$ the chromatic number. If $f(n)$ is the maximum value of $\chi(G)/\omega(G)$, as $G$ ranges over all graphs on $n$ vertices, then does
$$\lim_{n\to\infty}\frac{f(n)}{n/(\log n)^2}$$
exist?

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