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).