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I was wondering what the relationship between the Ford-Fulkerson Method and the idea of min cuts is.
I understand that the max-flow min-cut theorem relates the the idea of min-cuts and the lack of an augmenting path to the max flow, and that the ford-fulkerson method relies on the idea of augmenting paths to find the max flow.
What I'm wondering is why did we need to introduce the idea of min-cuts at all?
It seems that all we need to know to calculate the max flow is the idea of residual networks, augmenting paths, and the Ford-Fulkerson Method.
Was the portion about max cuts added for completeness, or does the Ford-Fulkerson Method rely of the idea of min cuts somehow?
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