We consider the question of determining the probability of triangle count deviations in the Erdős-Rényi random graphs G(n, m) and G(n, p) with densities larger than \(n^{-1/2}(\log {n})^{1/2}\) . In particular, we determine the log probability \(\log \mathbb {P}\left( N_{\triangle }(G)\, >\, (1+\delta )p^3n^3\right) \) up to a constant factor across essentially the entire range of possible deviations, in both the G(n, m) and G(n, p) model. For the G(n, p) model, we also prove a stronger result, up to a \((1+o(1))\) factor, in the non-localised regime. We also obtain some results for the lower tail and for counts of cherries (paths of length 2).
