Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Fall 2017 MATH 1300-101
Last updated: October 2017
Comments and suggestions: Email wim.ruitenburg@marquette.edu
Book, chapter 5 on Euler paths
This book chapter mostly considers graphs with possibly multiple edges between
the vertices.
We also write node instead of vertex, or nodes instead of vertices.
All edges are undirected.
We attempt to walk the graph by using each edge just once, preferably ending
at our starting point.
- Graphs may or may not be connected.
- Vertices may or may not be adjacent.
- Parts of a graph may be connected by a bridge.
- The degree of a vertex is...
- The length of a path is...
- What is a component of a graph?
- And so on.
The main results appear to be:
- An Euler circuit exists if and only if...
- An Euler path exists if and only if...
- If an Euler path exists, then its endpoints are...
- The Euler sum of degrees theorem on page 180.
- Fleury's algorithm on page 182.
- Eulerizing a graph.
Example Problems
- Recommended problems from Chapter 5 of the book:
2, 8, 9
- Recommended problems from Chapter 5 of the book:
11, 30ab, 36, 69