(Latest Revision: Apr 23, 2021)

Solution to the 2021 Flow Network Problem

flow problem solution, page 01
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For this problem, the minimum cut consists of just the source node. No other nodes are reachable in the final version of the residual graph, Gf. The capacity of the cut is the sum of the capacities of the edges leaving the source, 3 + 4 + 5 = 12. The value of the max flow is the sum of the flows on the edges leaving the source. That sum is also 3 + 4 + 5 = 12. These calculations verify that the max value of an s-t flow is equal to the min capacity of an s-t cut, which, according to the "Max-Flow, Min-Cut Theorem," is true for any flow network.