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A trail is a walk in which all edges are distinct. [2] A path is a trail in which all vertices (and therefore also all edges) are distinct. [2] If w = (e 1, e 2, …, e n − 1) is a finite walk with vertex sequence (v 1, v 2, …, v n) then w is said to be a walk from v 1 to v n. Similarly for a trail or a path.
A country track, or fieldway, in Slovenia Mountain bike trail in the Forest of Dean, England Trail in the Kruununpuisto Nature Park in Imatra, Finland. A trail, also known as a path or track, is an unpaved lane or a small paved road not intended for usage by motorized vehicles, usually passing through a natural area.
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex .
A trailhead signage that shows the grade of a walking path at a park in Sydney, Australia.. A trail difficulty rating system, also known as walking track grading system, walk gradings or trail grades, is a classification system for trails or walking paths based on their relative technical and physical difficulty. [1]
A desire path, often referred to as a desire line in transportation planning and also known by various other names, [a] is an unplanned small trail created as a consequence of mechanical erosion caused by human or animal traffic. The path usually represents the shortest or the most easily navigated route between an origin and destination, and ...
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An early example of an interest in hiking in the United States is Abel Crawford and his son Ethan's clearing of a trail to the summit of Mount Washington, New Hampshire in 1819. [37] This 8.5-mile path is the oldest continually used hiking trail in the United States.
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