Jim Olsen: Euler and Hamiltonian Path and Circuits

This article is an in-depth look at graphs. Topics covered are graph models, terminology, representations of graphs, graph isomorphism, connectivity, Euler and Hamiltonian Paths, and more. Examples and explanations are included.

In this Unit, you will use vertex-edge graphs and Euler Circuits to help find optimum paths. Included are two lessons that help you develop the understanding and skill needed to solve problems about optimum paths and conflicts.

In this geometry learning exercise, students analyze different polygons and relate it to a circuit board. They find the odd degree Euler circuit and identify the vertices of the odd degree. There are 3 questions with an answer key.

In this math worksheet, high schoolers match math vocabulary to definitions and then solve problems using Euler's theorem and Fleury's algorithm. Students complete 24 problems.

Brief description of Hamiltonian Path and solving the Hamiltonian Path problem.

Explanation and questions about Euler paths and circuits with solutions to the questions.

A description of a Hamiltonian path, also called a Hamilton path.

Students explore the concept of euler paths and circuits. For this euler paths and circuits lesson, students discuss the bridges of Königsberg problem. Students discuss how to determine if an euler circuit exists. Students discuss the...

Basic introduction of Euler circuits and paths using models to define each, describe the difference between them, and how to tell which you have on a given graph.

Contains a clear explanation of the basic terminology of graph theory. The useful for a first introduction to graphs and graph theory.