The fractional chromatic number of the direct product of graphs

This paper discusses the fractional chromatic number of the direct product of graphs. It is proved that if His a circulant graph G^k_d, or a Kneser graph, or a direct sum of such graphs, then for any graph G, \chi_f{\hskip1}(G\times H{\hskip1}) = {\text min}\{\chi_f{\hskip1}(G), \chi_f{\hskip1}(H{\hskip1})\}.