On the Ramsey multiplicity of complete graphs

We show that, for n large, there must exist at least $$frac{{n^t }} {{C^{(1 + o(1)t^2 } )}}$$ monochromatic K _t s in any two-colouring of the edges of K _n , where C??2.18 is an explicitly defined constant. The old lower bound, due to Erd?s [2], and based upon the standard bounds for Ramsey??s theorem, is $$frac{{n^t }} {{4^{(1 + o(1)t^2 } )}}. $$