CSE3500 - HW4.pdf - CSE 3500 Algorithms and Complexity...

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CSE 3500 Algorithms and Complexity February 23, 2016 Homework 4 1. (K&T Ch. 4 question 8) Suppose you are given a connected graph G with edge costs that are all distinct. Prove that G has a unique minimum spanning tree. 2. Suppose we have a graph G , where all but two of the edges have distinct weights – that is, two edges have the same weight, and all of the others are distinct. Which of these is true: a) G has a unique MST, b) G has more than one MSTs, or c) Sometimes G has a single MST, sometimes G has more than 1 MST. Prove your answer is correct. 3. A Minimum-Bottleneck Spanning Tree (MBST) is a spanning tree of a connected undirected graph with positive edge weights chosen so its maximum edge weight is as small as possible.
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  • Fall '19
  • Graph Theory, Planar graph, Vertex-transitive graph, graph G

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