Definition:Trail
Jump to navigation
Jump to search
Definition
A trail is a walk in which all edges are distinct.
A trail between two vertices $u$ and $v$ is called a $u$-$v$ trail.
Subgraph
The set of vertices and edges which go to make up a trail in a graph $G$ form a subgraph of $G$.
This subgraph itself is also referred to as a trail in $G$.
Also known as
A trail can also be seen referred to as an Eulerian walk, for Leonhard Paul Euler.
Also see
- Definition:Circuit (Graph Theory), otherwise known as a Definition:Closed Trail
- Results about trails can be found here.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.3$: Connected Graphs
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trail
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): walk
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trail
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): walk
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): trail