# Definition:Semi-Eulerian Graph

(Redirected from Definition:Traversable Graph)

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## Definition

A graph is called **semi-Eulerian** if and only if it contains an Eulerian trail.

Note that the definition of graph here includes:

Note that an Eulerian graph is also **semi-Eulerian**, as an Eulerian circuit is still a path, and therefore an Eulerian trail.

## Also known as

A **semi-Eulerian graph** is also called a **traversable graph**.

Some sources have **transversable graph** but it is suspected that this is a mistake.

## Also see

- Results about
**Eulerian graphs**can be found here.

## Source of Name

This entry was named for Leonhard Paul Euler.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 3.1$: The Königsberg Bridge Problem: An Introduction to Eulerian Graphs - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**transversable graph**