SCHWEITZER 2004 Problem 2

Write $t(G)$ for the number of complete quadrilaterals in the graph $G$ and $e_G(S)$ for the number of edges spanned by a subset $S$ of vertices of $G$ . Let $G_1, G_2$ be two (simple) graphs on a common underlying set $V$ of vertices, $|V|-n$ , and assume that $|e_{G_1}(S)-e_{G_2}(S)|<\frac{n^2}{1000}$ holds for any subset $S\subseteq V$ . Prove that $|t(G_1)-t(G_2)|\le \frac{n^4}{1000}$ .