## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.2 Euler Paths and Euler Circuits - Exercise Set 14.2 - Page 913: 71

#### Answer

The original statement does not make sense.

#### Work Step by Step

The original statement does not make sense. According to Euler's theorem, if a graph has zero odd vertices, then the graph has at least one Euler path and at least one Euler circuit. If a graph has exactly two odd vertices, then the graph has at least one Euler path. We can use Euler's theorem to determine if a graph has Euler paths or Euler circuits. If we know that an Euler path or an Euler circuit exists in the graph, we can use Fleury's Algorithm to find the specific Euler paths or Euler circuits. This algorithm gives us a method to find Euler's paths or Euler's circuits in a graph if we know that an Euler path or an Euler circuit exists in the graph. However, we do not use Fleury's Algorithm to determine if a graph contains Euler paths or Euler circuits.

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