Erdős's colorability threshold conjecture for sparse random graphs

Fix an integer $k\geq 2$, and let $G(n,cn)$ be the sparse random graph with $n$ vertices and $cn$ edges. The graph is $k$-colorable when its vertices can be assigned colors $1,2,\ldots,k$ so that adjacent vertices receive different colors. Erdős's colorability threshold conjecture. For every positive integer $k\geq 2$ there exists a critical value $c^*_k$ such that $G(n,cn)$ is $k$-colorable with high probability when $c<c^*_k$ and is not $k$-colorable with high probability when $c>c^*_k$. The source presents this as an open scaling-limit question and attributes it to Erdős via Alon and Spencer.