## Graph Theory

Given an undirected graph $G=(V,E)$ and two vertices $u$ and $v$, if the minimum number of edges connecting $u$ and $v$ is greater than $\frac n2$ (where $n=|V|$), show there exists a node $w\neq u,v$ such that all $u$- $v$ paths contain $w$.

I'm not sure how to get started but something tells me to use breadth first search and apply the pigeon hole principle.

Any help is appreciated! Thanks!