For integers $n,k\in\mathbb N$ with $n\ge 2k$,
\begin{align*}
\chi(SG(n,k)) = n-2k+2.
\end{align*}
Moreover, $SG(n,k)$ is vertex-critical: deleting any vertex lowers the chromatic number.
Knowledge Status
Discrete MathematicsCombinatorics
Discussion
Schrijver Theorem: For integers n,k N with n 2k, align* (SG(n,k)) = n-2k+2.