Planting colourings silently
Combinatorics, Probability & Computing, Volume abs/1411.0610, Issue 3, 2017.
Let $k\geq3$ be a fixed integer and let $Z_k(G)$ be the number of $k$-colourings of the graph $G$. For certain values of the average degree, the random variable $Z_k(G(n,m))$ is known to be concentrated in the sense that $\frac1n(\ln Z_k(G(n,m))-\ln E[Z_k(G(n,m))])$ converges to $0$ in probability [Achlioptas and Coja-Oghlan: FOCS 2008]...More
PPT (Upload PPT)