Let be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut of is any nontrivial subset of , and the weight of the cut is the sum of weights of edges crossing the cut. A mincut is then defined as a cut of of minimum weight. The problem is polynomial time solvable as a series of network flow problems or using the algorithm of Stoer and Wagner (1994).

# Mincut

## See also

Boolean Function, Cut, Maxcut, Minimum Vertex Cut, Network Flow, Weighted Graph## Explore with Wolfram|Alpha

## References

Stoer, M. and Wagner, F. "A Simple Min Cut Algorithm."*Algorithms--ESA '94, LNCS 855*, 141-147, 1994.

## Referenced on Wolfram|Alpha

Mincut## Cite this as:

Weisstein, Eric W. "Mincut." From *MathWorld*--A
Wolfram Web Resource. https://mathworld.wolfram.com/Mincut.html