Graph contains triangle Prove that if a simple graph of order n has more than n^2/4 edges then it contains a triangle.
I know Martels theorem states the opposite condition for a triangle free graph but I'm not sure how to prove this condition.

Let $G$ be a simple graph of order $n$. Then Mantel's Theorem states that:

If $G$ is triangle-free, then $G$ has at most $n^2/4$ edges.

But by taking the contrapositive of this implication, we get exactly what we want:

If $G$ has more than $n^2/4$ edges, then $G$ contains a triangle.

