Trail

Definition

Let $G$ be a graph. A trail in $G$ is a walk $(w_0, w_1, \dots, w_k)$ whose edges $w_0 w_1, w_1 w_2, \dots, w_{k-1} w_k$ are pairwise distinct.

Remarks

A trail may visit a vertex more than once, but it uses each edge at most once. Every path is a trail. In the graph of two triangles that share a vertex $c$, the closed walk $a, b, c, d, e, c, a$ is a trail but not a path. An Eulerian trail is a trail that uses every edge.

Explanations

L1 human

A trail is a walk that never uses the same edge twice. It is the kind of route that you draw without lifting your pen and without retracing a line.