Editing Menger's theorem (section)

==Vertex connectivity==
The '''vertex-connectivity''' statement of Menger's theorem is as follows:

:Let ''G'' be a finite undirected graph and ''x'' and ''y'' two [[nonadjacent]] vertices. Then the size of the minimum [[vertex cut]] for ''x'' and ''y'' (the minimum number of vertices, distinct from ''x'' and ''y'', whose removal disconnects ''x'' and ''y'') is equal to the maximum number of pairwise [[path (graph theory)|internally disjoint paths]] from ''x'' to ''y''.

A consequence for the entire graph ''G'' is this version:

:A graph is [[K-vertex-connected graph|''k''-vertex-connected]] (it has more than ''k'' vertices and it remains connected after removing fewer than ''k'' vertices) if and only if every pair of vertices has at least ''k'' internally disjoint paths in between.