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## Google Colab.

qThat is, after removing all the edges of C, we can partition the vertices of G into two subsets, A, and B such that there are no edges between a vertex in A and a vertex in B.

qA minimum cut of G is a cut of smallest size among all cuts of G. Minimum Cuts 2 Minimum Spanning Tree 5/6/17 2. Greedy Property:The minimum weight edge crossing a cut is in the minimum spanning tree.

### Maze generation.

Proof Idea:Assume not, then remove an edge crossing the cut and replace it with the minimum weight edge. RestatementLemma:Let G= (V;E) be an undirected graph with edge weights w. Let A E be a set of edges that are part of a minimum spanning tree. Apr 06, A Minimum Spanning Tree(MST) or minimum weight spanning tree for a weighted, connected, undirected graph is a spanning tree having a weight less than or equal to the weight of every other possible spanning tree.

The weight of a spanning tree is the sum of weights given to each edge of the spanning tree. Reverse-Delete algorithm produces a minimum spanning tree. v u e = (u,v) Because removing e won't disconnect the graph, there must be another path between u and v Because we're removing in order of decreasing weight, e must be the largest edge on that bushcutting.bar Size: KB.

Properties of Spanning Tree: There may be several minimum spanning trees of the same weight having the minimum number of edges. If all the edge weights of a given graph are the same, then every spanning tree of that graph is minimum.

If each edge has a distinct weight, then there will be only one, unique minimum spanning tree. A connected graph G can have more than one spanning trees. Oct 10, Following are steps to print all edges of the minimum 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.