Stahl's Kneser graph homomorphism conjecture

Let $n,k,k'$ be integers, and write $k'=qk-r$ with $0\leq r<k$. Let $\operatorname{KG}(n,k)$ denote the Kneser graph on the $k$-subsets of $[n]$. Stahl's Kneser graph homomorphism conjecture. There is a graph homomorphism $\operatorname{KG}(n,k)\to\operatorname{KG}(n',k')$ if and only if $n'\geq qn-2r$. The source calls this broadly open.