Consider the following algorithm. Input: A connected graph G. Output: A spanning tree of
Chapter 50, Problem 50.17(choose chapter or problem)
Consider the following algorithm. Input: A connected graph G. Output: A spanning tree of G. (1) Let T be a graph with the same vertices as G, but with no edges. (2) Let e1; e2; : : : ; em be the edges of G. (3) For k D 1; 2; : : : ; m, do: (3a) If adding edge ek to T does not form a cycle with edges already in T , then add edge ek to T . (4) Output T . Prove that this algorithm is correct. In other words, prove that whenever the input to this algorithm is a connected graph, the output of this algorithm is a spanning tree of G
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