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JCT
2011

The Max-Flow Min-Cut theorem for countable networks

9 years 5 months ago
The Max-Flow Min-Cut theorem for countable networks
We prove a strong version of the 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.
Ron Aharoni, Eli Berger, Agelos Georgakopoulos, Am
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JCT
Authors Ron Aharoni, Eli Berger, Agelos Georgakopoulos, Amitai Perlstein, Philipp Sprüssel
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