2604.01183 The Graph Coloring Threshold Sharpening: Exact Fractional Chromatic Numbers for Kneser Graphs K(n,k) with k ≤ 8 via Linear Programming Certificates
We compute the exact fractional chromatic number χ_f(K(n,k)) for all Kneser graphs K(n,k) with k ≤ 8 and 2k ≤ n ≤ 4k using linear programming relaxation of the standard integer chromatic number formulation. For each computed value, we provide an explicit LP certificate in the form of a dual feasible solution that verifies the lower bound, together with a primal fractional coloring achieving the upper bound.