Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.2 Euler Paths and Euler Circuits - Exercise Set 14.2: 69

Answer

The original statement makes sense. I'm working with a graph whose vertices are all even, so an Euler circuit must exist.

Work Step by Step

The original statement makes sense. I'm working with a graph whose vertices are all even, so an Euler circuit must exist. According to Euler's theorem, if a graph has no odd vertices, then the graph has at least one Euler circuit. If a graph has vertices which are all even, then the number of odd vertices is zero. Therefore, according to Euler's theorem, there is at least one Euler circuit in the graph.
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