Menger's theorem

In the mathematical discipline of graph theory and related areas Menger's theorem is a basic result about connectivity in finite undirected graphs. It was proved by Karl Menger in 1927 and later generalized by the max flow min cut theorem.

Let G be a finite undirected graph and x and y two nonadjacent vertices. Then the theorem states that the size of the minimum vertex cut for x and y (the minimum number of vertices whose removal disconnects x and y) is equal to the maximum number of pairwise vertex independent paths from x to y.