  With $\xi$ the number of triangles in the usual (Erd\H{o}s-R\'enyi) random
graph $G(m,p)$, $p>1/m$ and $\eta>0$, we show (for some $C_{\eta}>0$)
$$\Pr(\xi> (1+\eta)\E \xi) < \exp[-C_{\eta}\min{m^2p^2\log(1/p),m^3p^3}].$$
This is tight up to the value of $C_{\eta}$.
