Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 17F / b / Solution

Let $T$ be the number of triangles. Each edge $uv$ has at least
$d(u)+d(v)-n$ common neighbours, and summing common-neighbour counts over edges counts every triangle three times. HenceIf $e>(1+\delta )n^2/4$, this is greater than
$\delta en>\delta n^3/4$. Thereforeso one may take $\epsilon =\delta /12$.