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Corollary 27.4

If flow network G has flow f, augmenting path p in Gf, and \(f' \;=\; f \;+\; f_p\), then f' is a flow in G with value \(\mid f' \mid \;=\; \mid f \mid \;+\; \mid f_p \mid \;>\; \mid f \mid\).

So, keep adding augmenting paths until there are no more.

Theorem 27.2

f is a maximum flow in G if and only if residual network Gf has no augmenting paths.

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