Meunier's chromatic number conjecture for stable Kneser graphs

Let $KG(n,k)_{s-\mathrm{stab}}$ be the induced subgraph of the Kneser graph $KG(n,k)$ on the $s$-stable $k$-subsets of $[n]$, where a subset $A$ is $s$-stable when $s\leq |i-j|\leq n-s$ for every pair of distinct elements $i,j\in A$. Meunier's conjecture. If $n,k,s$ are non-negative integers such that $n\geq sk$ and $s\geq 2$, then

$$\chi\left(KG(n,k)_{s-\mathrm{stab}}\right)=n-s(k-1).$$

This generalizes the chromatic-number formula for Schrijver graphs, which are the case $s=2$. The source presents the assertion as Meunier's conjecture; no resolution is given in the supplied text.