The Max-Flow Min-Cut Theorem for Countable Networks

Details The Max-Flow Min-Cut Theorem for Countable Networks The Max-Flow Min-Cut Theorem for Countable Networks

2009-11-20

arxiv.org/abs/0911.4003v1

Mathematics

Combinatorics

19 pages, to be published in Journal of Combinatorial Theory, Series B

Scientific paper

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are "orthogonal" to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.

Affiliated with

Also associated with

No associations

Rating

The Max-Flow Min-Cut Theorem for Countable Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Max-Flow Min-Cut Theorem for Countable Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Max-Flow Min-Cut Theorem for Countable Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-432081