J - Vertex Separation

Consider an undirected graph. A pair of vertices $(u, v)$ are said to be *separated* if the following condition holds: - There exist two simple paths, both from $u$ to $v$, whose lengths differ by *at least* $2$. Note that a simple path is a path where all vertices are distinct. A vertex $u$ is said to be *separable* if there exists at least one other vertex $v$ such that the pair $(u, v)$ is sep