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$$\underset{n\to \infty }{\lim }\frac{f(n)}{n/({\log }_{2}n{)}^2}$$exist?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **not known** in general: the existence of [ \lim_{n\to\infty}\frac{f(n)}{n/(\log n)^2} ] is an **open Erdős problem** (often listed as Erdős Problem #627). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.