 Solution

The vertex version of Menger's theorem states that for two distinct nonadjacent vertices $s,t$ of a finite graph, the maximum number of internally vertex-disjoint $s$-$t$ graph paths equals the minimum size of a set $S\subseteq V\setminus \{s,t\}$ whose deletion separates $s$ from $t$.Internally disjoint graph paths may share their endpoints but no other vertex. The nonadjacency hypothesis is needed in this separator formulation, since an edge $st$ cannot be destroyed by deleting other vertices.