Problem 627

Erdős Problem #627: declared status 'open'. Formalized: no. 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? Prize: no. Tags: chromatic number, graph theory.