Compute the max flow for the following diagram, using the Ford-Fulkerson algorithm.

enter image description here

I computed the max flow, using the Ford-Fulkerson algorithm, and I got 14. However, the capacity of the min cut I found is 16, which does not verify the max-flow/min-cut theorem. Otherwise, if I did something wrong in finding the min-cut and/or max flow, let me know. It took me so much hours to work out this problem.

  • $\begingroup$ Can you show us your work? Perhaps we can spot an error in your work. $\endgroup$ – ml0105 May 5 '14 at 4:19

Max flow is 14. The cut partition is $\{B, C, D, G\}$ indicated in Green to $\{A, E, F, H\}$ indicated in Purple. Cut edges are indicated in red. By Max-Flow Min-Cut Theorem, the simultaneous existence of a cut of capacity 14 and a flow of capacity 14 proves this optimum.

Labeled graph

You can verify by looking at the validity of the flow by comparing the ingress and egress flow of each vertex.

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