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The max-flow min-cut theorem for countable networks
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Aharoni, Ron, Berger, Eli, Georgakopoulos, Agelos, Perlstein, Amitai and Sprüssel, Philipp (2011) The max-flow min-cut theorem for countable networks. Journal of Combinatorial Theory, Series B, Vol.101 (No.1). pp. 1-17. doi:10.1016/j.jctb.2010.08.002 ISSN 0095-8956.
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Official URL: http://dx.doi.org/10.1016/j.jctb.2010.08.002
Abstract
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Combinatorial Theory, Series B | ||||
Publisher: | Academic Press | ||||
ISSN: | 0095-8956 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.101 | ||||
Number: | No.1 | ||||
Page Range: | pp. 1-17 | ||||
DOI: | 10.1016/j.jctb.2010.08.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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