A special case of the Stahl conjecture

Let Gn,k denote the Kneser graph whose vertices are the n-element subsets of a (2n+k)-element set and whose edges are the disjoint pairs. In this paper we prove that for any non-negative integer s there is no graph homomorphism from G4,2 to G4s+1,2s+1. This confirms a conjecture of Stahl in a special case.