Definition:Eulerian Trail

Definition

An Eulerian trail is a trail $T$ that passes through every vertex of a graph $G$ and uses every edge of $G$ exactly once.

Also known as

An Eulerian trail is also known as an Eulerian path by treatments which define a path how $\mathsf{Pr} \infty \mathsf{fWiki}$ defines a trail.

Also seen are the following:

• Euler path
• Euler trail
• Eulerian chain or Euler chain

An Eulerian trail is said to traverse $G$.

Also see

• Definition:Semi-Eulerian Graph

• Definition:Eulerian Circuit

• Eulerian Circuit is Eulerian Trail

• Results about Eulerian trails 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
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): chain: 4.
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Eulerian (or Euler) chain or trail
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Eulerian trail