Local convergence of random graph colorings

Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari

Let $G=G(n,m)$ be a random graph whose average degree $d=2m/n$ is below the $k$-colorability threshold. If we sample a $k$-coloring $\sigma$ of $G$ uniformly at random, what can we say…