Menger's theorem

Menger's theorem --- теорема Менгера.

1. (An edge-form of the theorem). Let [math]\displaystyle{ G }[/math] be an unoriented graph with two distinguished vertices [math]\displaystyle{ s }[/math] and [math]\displaystyle{ t }[/math]. The maximum number of edge-disjoint paths joining [math]\displaystyle{ s }[/math] and [math]\displaystyle{ t }[/math] is equal to the minimum number of edges in a cut separating [math]\displaystyle{ s }[/math] and [math]\displaystyle{ t }[/math].

2. (A vertex-form of the theorem). The minimum number of vertices separating two nonadjacent nodes [math]\displaystyle{ s }[/math] and [math]\displaystyle{ t }[/math] is equal to the maximum number of vertex disjoint [math]\displaystyle{ s - t }[/math] paths.