# Maximum flow

Is it true that if I multiply all the edge capacities in an s-t flow problem by a positive constant k > 0, then the maximum flow increases by the same factor of k.

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#### Solution Preview

Yes it is

Because,

the sum of the capacities of the arcs on the minimal cut equals the maximum flow is a famous theorem of network theory called the max flow min cut theorem

for example

Let minimal cuts of arcs in s-t flow are ...

#### Solution Summary

This verifies a statement regarding edge capacities and maximum flow.

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