I was wondering what the relationship between the Ford-Fulkerson Method and the

Question

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?

Explanation / Answer

from the question the minimum cut used in the Ford-Fulkerson Method is used to find the saturated edges.the flow of the edges is given within the capacity limits which may be equal to the capacity so the edges are the minimum cut in the graph the maximum cut is used to find all the subset of the graph let us say S which is used to find all the path complementary subset as much as possible in a large network this always occur for NP complete problem the min cut solves the vertex pair with minimum possible weight in the undirected graph.

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