Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3 - Page 923: 62


The original statement does not make sense.

Work Step by Step

The original statement does not make sense. An Euler circuit is a circuit in a graph that travels through every edge of a graph exactly once. To pick up all the garbage in the city, workers need to travel along every street in the city. In order to do this efficiently, it would be a good idea to follow an Euler circuit which travels through every edge in a circuit exactly once. A Hamilton circuit visits every vertex in a graph exactly once. However, a Hamilton circuit does not necessarily travel along every edge in a graph. If workers followed a Hamilton circuit, they would not travel along every street in a city and there would be a lot of garbage which would not get picked up. The solution to a traveling salesperson problem is a Hamilton circuit. Therefore, city planners do not need to solve a traveling salesperson problem to determine efficient routes along city streets for garbage pickup.
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