Vertex exposure for chromatic number ($\mathrm{Pr}(|\chi -\mathbb{E}\chi |\ge \lambda \sqrt{n})\le 2e^{-2{\lambda }^2}$)

Group random edges by their larger endpoint. These independent coordinates each change edges incident to only one vertex. Removing that vertex leaves the same graph under any two outcomes, so their chromatic numbers differ by at most one. The McDiarmid inequality with $n$ coordinate ranges of length one gives the displayed concentration bound.