Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 17H / a / Solution

The vertex form of Menger theorem states that if $x$ and $y$ are distinct nonadjacent vertices of a finite graph, then the maximum number of pairwise internally vertex-disjoint paths from $x$ to $y$ equals the minimum cardinality of an $x$-$y$ vertex separator.