GATE | GATE CS 1999 | Question 53

[5 Marks question]

Let G be a connected, undirected graph. A cut in G is a set of edges whose removal results in 0 being broken into two or more components which are not connected with each other. The size of a cut is called its cardinality. A men-cut of G is a cut in G of minimum cardinality. Consider the following graph.


a.  Which of the following sets of edges is a cut?

(i) {(A,B), (E,F), (B,D), (A,E), (A,D)}

(ii)  {(B,D), (C,F), (A,B)}

b.  What is the cardinality of a min-cut in the graph?

c.  Prove that if a connected undirected graph G with n vertices has a min-cut of cardinality K, then G has atleast  (nk/2) edges.



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