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Title of article :
The Max-Flow Min-Cut theorem for countable networks
Author/Authors :
Aharoni، نويسنده , , Ron and Berger، نويسنده , , Eli and Georgakopoulos، نويسنده , , Agelos and Perlstein، نويسنده , , Amitai and Sprüssel، نويسنده , , Philipp، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
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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 Kirchhoffʹs first law also for ends.
Keywords :
flows , Max-flow min-cut , ends of graphs , Infinite graphs , Networks
Journal title :
Journal of Combinatorial Theory Series B
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