Chromatic number conjecture for powers of cycle Kneser hypergraphs

For integers $n\geqslant s\geqslant2$ with $n>ks$, let $C_n^{s-1}$ be the $(s-1)$-st power of the cycle of length $n$, and let $K(n,k,s)$ be the $s$-uniform hypergraph whose vertices are the independent $k$-sets of $C_n^{s-1}$, with an edge formed by every $s$ pairwise disjoint such sets. Chromatic number conjecture. For $n>ks$,

$$\chi\bigl(K(n,k,s)\bigr)=\left\lceil\frac{n-ks+s}{s-1}\right\rceil.$$

The paper attributes this conjecture to Alon, Dol'nikov and collaborators and notes that it is proved when $s$ is a power of $2$; the general case remains open.