## What is minimum cut in Ford-Fulkerson?

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.

**How is Max flow equal to min-cut?**

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 …

**What is maximum flow in Ford-Fulkerson?**

The capacity for forward and reverse paths are considered separately. Adding all the flows = 2 + 3 + 1 = 6, which is the maximum possible flow on the flow network.

### Is there only one min-cut?

Look at the group of vertices reachable from t in the reverse direction of the arrows (meaning all the vertices which can reach t). This group is also a min-cut. If that cut is identical to your original cut, then there is only one. Otherwise, you just found 2 cuts, so the original one can’t possibly be unique.

**What is the min-cut?**

Min-Cut of a weighted graph is defined as the minimum sum of weights of (at least one)edges that when removed from the graph divides the graph into two groups.

**Does Ford-Fulkerson algorithm use the idea of?**

Explanation: Ford-Fulkerson algorithm uses the idea of residual graphs which is an extension of naïve greedy approach allowing undo operations.

#### Why is Ford-Fulkerson polynomial time?

Yes, the Ford-Fulkerson algorithm is a pseudopolynomial time algorithm. Its runtime is O(Cm), where C is the sum of the capacities leaving the start node. Since writing out the number C requires O(log C) bits, this runtime is indeed pseudopolynomial but not actually polynomial.

**What is cut and Min-cut?**

In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric.

**Is min cut in NP?**

We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3.

## Where is Fulkerson min cut?

1) Run Ford-Fulkerson algorithm and consider the final residual graph. 2) Find the set of vertices that are reachable from the source in the residual graph. 3) All edges which are from a reachable vertex to non-reachable vertex are minimum cut edges. Print all such edges.