Menger's Theorem
In the
mathematical
discipline of
graph theory
and related areas
Menger's theorem
is a basic result about
connectivity
in
finite undirected graphs
. It was proved by
Karl Menger
in 1927 and later generalized by the
max flow min cut theorem
. Let
G
be a finite undirected graph and
x
and
y
two
nonadjacent
vertices. Then the theorem states that the size of the minimum
vertex cut
for
x
and
y
(the minimum number of vertices whose removal disconnects
x
and
y
) is equal to the maximum number of pairwise
vertex independent paths
from
x
to
y
.
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