Why is max-flow min-cut theorem?

The max-flow min-cut theorem states that the maximum flow through any network from a given source to a given sink is exactly equal to the minimum sum of a cut. This theorem can be verified using the Ford-Fulkerson algorithm. This algorithm finds the maximum flow of a network or graph.

What is the capacity of the minimum st cut?

The minimum s-t cut is {{1, 3}, {4, 3}, {4 5}} which has capacity as 12+7+4 = 23. Try It! We strongly recommend to read the below post first. Like Maximum Bipartite Matching, this is another problem which can solved using Ford-Fulkerson Algorithm.

What do you mean by maximal flows and minimal cuts explain the Maxflow min cut theorem with suitable example?

In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would disconnect the source …

Why is it called Min cut?

The minimum cut problem (abbreviated as “min cut”), is defined as follows: Input: Undirected graph G = (V,E) Output: A minimum cut S, that is, a partition of the nodes of G into S and V \ S that minimizes the number of edges going across the partition.

Is max flow NP complete?

The maximum flow problem with minimum quantities was introduced in [4], where the problem was shown to be weakly NP-complete even on series-parallel graphs and Lagrangean relaxation techniques and heuristics for solving the problem were studied.

What is Ford-Fulkerson algorithm explain with example?

The Ford-Fulkerson algorithm is used to detect maximum flow from start vertex to sink vertex in a given graph. In this graph, every edge has the capacity. Two vertices are provided named Source and Sink. The source vertex has all outward edge, no inward edge, and the sink will have all inward edge no outward edge.

What do you mean by maximal flows and minimal cuts explain the Maxflow min-cut theorem with suitable example?