A sharp threshold for random graphs with a monochromatic triangle in every edge coloring

Let R be the set of all finite graphs G with the Ramsey property that every coloring of the edges of G by two colors yields a monochromatic triangle. In this paper we establish a sharp threshold for random graphs with this property. Let G(n,p) be the random graph on n vertices with edge probability p. We prove that there exists a function b =b(n) = �(1) such that for any " > 0, as n tends to infinity,

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