Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Spring 2010 MATH 1300-101
Book, chapter 5 on Euler paths
This book chapter mostly considers graphs with possibly multiple edges between
the 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.
- 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...
- Eulerizing a graph.
The following we did not talk much about in class:
- The Euler sum of degrees theorem.
- Fleury's algorithm.
Last updated: April 2010
Comments and suggestions: Email wimr@mscs.mu.edu