Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 17G / iii / Solution

Let $t(G)$ be the number of triangles in a graph. Count incidences $(e,\Delta )$ in which the edge $e$ lies in the triangle $\Delta$. Every edge contributes at least one incidence by hypothesis, while every triangle contributes exactly three. ThereforeThis is the edge-triangle incidence bound.