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Fall Semester 2008 CS300 Algorithms
Homework #7 (due 11/21)
1. A connected graph is
edgebiconnected
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 edgebiconnected.
(b) An edgebiconnected 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
minimumbottleneck spanning tree
if there is no spanning tree
T
0
of
G
with a cheaper bottleneck edge.
(a) Is every minimumbottleneck 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.
 Spring '08
 Unkown
 Algorithms

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