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

Here $|V(G)|=2n$ and $e(G)=n^2+1$. By Mantel theorem, a triangle-free graph of this order has at mostedges, so $G$ contains a triangle in a graph.

If $n=2$, then $G$ has four vertices and five of the six possible edges, so it is $K_4$ with one edge deleted. Exactly the two triangles containing neither both endpoints of the deleted edge remain. Hence $G$ contains two triangles.