Editing Menger's theorem (section)

==Edge connectivity==
The '''edge-connectivity''' version of Menger's theorem is as follows:

:Let ''G'' be a finite undirected graph and ''x'' and ''y'' two distinct vertices. Then the size of the minimum [[Edge cut#Connectivity|edge cut]] for ''x'' and ''y'' (the minimum number of edges whose removal disconnects ''x'' and ''y'') is equal to the maximum number of pairwise [[path (graph theory)#Examples|edge-disjoint path]]s from ''x'' to ''y''.

The implication for the graph ''G'' is the following version:

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