Vertex exposure for chromatic number
= Vertex exposure for chromatic number
{title2=$\Pr(|\chi-\mathbb E\chi|\ge\lambda\sqrt n)\le2e^{-2\lambda^2}$}
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.