Given a max flow s-t in a network R, provide an algorithm to find the cut of max capacity.

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By applying an algorithm we can find the max flow in a network.

Is there a way to find the max capacity cut in O(m) from the residual graph of the max flow?

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A flow $f$ is maximum if and only if the residual graph is disconnected. In this case, the vertices in $S$ are the ones reachable from the source node. The remaining vertices are in $T$.

A graph traversal algorithm like BFS will find these edges.