The gap between monotone and non-monotone circuit complexity is exponential

A. A. Razborov has shown that there exists a polynomial time computable monotone Boolean function whose monotone circuit complexity is at leastn^{c losn}. We observe that this lower bound can be improved to exp(cn^1/6–o(1)). The proof is immediate by combining the Alon—Boppana version of another argument of Razborov with results of Grötschel—Lovász—Schrijver on the Lovász — capacity, of a graph.