Department of Mathematical and Statistical Sciences
Wim Ruitenburg's Fall 2024 MATH 1300-101
Last updated: 24 November 2024
Comments and suggestions:
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, possibly ending
at our starting point.
- Vertices may or may not be adjacent.
- The length of a path is...
- Graphs may or may not be connected.
- What is a component of a graph?
- Parts of a graph may be connected by a bridge.
- The degree of a vertex is...
- And so on.
For us, an Euler circuit is a special kind of Euler path.
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 but is not a circuit, then its endpoints are...
- The Euler sum of degrees theorem.
- Fleury's algorithm if an Euler path is possible.
- 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, 36, 43, 60 (tricky)