AbstractThe m‐chromatic number χm(G) of a graph G is the fewest colors needed so each node has m colors and no color appears on adjacent nodes. The fractional chromatic number is χ*(G)=limm→∞χm(G)/m. Let m(G) be the least m so that χ* (G) = χm(G)/m. For n node graphs, Chvátal, Garey and Johnson showed m(G) ≦ nn/2 and gave example, where m(G) is asymptotically magnified image. This note gives examples where m(G) is asymptotically λn, where λ ≈︁ 1.346193. © 1995 John Wiley & Sons, Inc.