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: 64

Answer

If the graph has no odd vertices, then the graph has at least one Euler circuit.

Work Step by Step

An odd vertex is a vertex with a degree that is an odd number. To determine if a graph has an Euler circuit, we need to determine the number of odd vertices in the graph. If the graph has no odd vertices, then the graph has at least one Euler circuit.
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