Stahl's multichromatic-number conjecture for Kneser graphs

Let $K(m,n)$ be the Kneser graph whose vertices are the $n$-subsets of $\{1,\ldots,m\}$, with two vertices adjacent when the corresponding subsets are disjoint. For an integer $r$, let $\chi_r(H)$ be the least integer $s$ such that $H$ admits a homomorphism to $K(s,r)$. Stahl's conjecture. If $k=an+b$, where $a\geq 1$ and $0\leq b\leq n-1$, then for $m\geq 2n$,

$$\chi_k(K(m,n))=\chi_{an}(K(m,n))+\chi_b(K(m,n))=(a+1)m-2(n-b).$$

This conjecture concerns the exact multichromatic numbers of Kneser graphs and is used in the paper to derive stronger lower bounds for chromatic numbers of exponential graphs. Its resolution is not specified in the supplied text.