Decide whether you think the following statement is true or false. If it is true, give a short explanation. If it is false, give a counterexample.
Let G be an arbitrary flow network, with a source s, a sink t, and a positive integer capacity ce on every edge e; and let (A, B) be a mimimum s-t cut with respect to these capacities {ce: e e E}. Now suppose we add 1 to every capacity; then (A, B) is still a minimum s-t cut with respect to these new capacities {1 + ce: e ε E}.
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