Nemotron-IMO-Bench 2026 C2

A graph $G$ has $n>1$ vertices. Prove that $$\sum_{e} \frac{c(e)}{c(e)-1}\leq \frac{n^2}{2},$$ the sum being taken over all edges of $G$ and $c(e)$ being the number of vertices of the largest complete subgraph of $G$ containing $e$.