# HW7 - Fall Semester 2008 CS300 Algorithms Homework #7 (due...

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Fall Semester 2008 CS300 Algorithms Homework #7 (due 11/21) 1. A connected graph is edge-biconnected if there is no edge whose removal disconnects the graph. Which, if either, of the following statements is true? Give a proof or counterex- ample for each. (a) A biconnected graph is edge-biconnected. (b) An edge-biconnected graph is biconnected. 2. One of the basic motivations behind the Minimum Spanning Tree Problem is the goal of designing a spanning tree for a set of nodes with minimum total cost. Here we explore another type of objective: designing a spanning tree for which the most expensive edge is as cheap as possible. Speciﬁcally, let G = ( V,E ) be a connected graph with n vertices, m edges, and positive edge costs that you may assume are all distinct. Let T = ( V,E 0 ) be a spanning tree of G ; we deﬁne the bottleneck edge of T to be the edge of T with the greatest cost. A spanning tree T of G is a minimum-bottleneck spanning tree if there is no spanning tree T 0 of G with a cheaper bottleneck edge. (a) Is every minimum-bottleneck tree of
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## This note was uploaded on 02/04/2010 for the course COMPUTER S cs300 taught by Professor Unkown during the Spring '08 term at Korea Advanced Institute of Science and Technology.

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