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Chapter 14: Problem 61

What is an Euler path?

Short Answer

Expert verified
An Euler path is a path in a graph which visits every edge exactly once. A graph has an Euler path if it is connected and exactly two vertices of the graph have odd degree. The odd degree vertices are the start and end of the Euler path.

Step by step solution

01

Definition

In graph theory, an Euler path is a path in a graph which visits every edge exactly once.
02

Characteristics

An Euler path can have any start and end vertex. It can pass through any other vertex more than once, but it must pass through every edge only once.
03

Applicability

A graph has an Euler path if it is connected and exactly two vertices of the graph have odd degree (number of edges). The odd degree vertices are the start and end of the Euler path.

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Most popular questions from this chapter

In Exercises 15-18, determine the number of Hamilton circuits in a complete graph with the given number of vertices. 12

In Exercises 49-52, draw a graph with the given characteristics. The graph has four even vertices.

Describe the relationship between the number of vertices and the number of edges in a tree.

Describe how to determine the number of Hamilton circuits in a complete graph.

Draw a graph with six vertices and two bridges.
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