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I need to find a linear algorithm (O(|V| + |E|) that would find the max flow on a graph where original max flow is known but the capacity of each edge is increased by 1.

user1255841
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If you know what the mincut is, I suppose you can just add one to the max flow for each cut edge.

John
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    I don't think that will work. You might have several min-cuts, with different number of edges crossing. If you choose the one with more edges, than the flow will still exceed capacity of the other min-cut. – user1255841 Apr 10 '12 at 18:06