Let be a graph with and two disjoint -tuples of graph vertices. Then either contains pairwise disjoint -paths, each connecting a point of and a point of , or there exists a set of fewer than graph vertices that separate and .
Harary (1994, p. 47) states the theorem as "the minimum number of points separating two nonadjacent points and is the maximum number of disjoint paths." Skiena (1990, p. 178) states the theorem as "a graph is k-connected graph iff every pair of vertices is joined by at least vertex-disjoint paths" (Menger 1927, Whitney 1932).