On a question of ErdH{o}s and Nev{s}etv{r}il about minimal cuts in a graph

Answering a question of Erd\H{o}s and Ne\v{s}et\v{r}il, we show that the maximum number of inclusion-wise minimal vertex cuts in a graph on $n$ vertices is at most $1.8899^n$ for large enough $n$.