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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.
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 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.
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 ...
The Knobstone Trail (KT) is Indiana's longest footpath – a 60-mile backcountry-hiking trail passing through Clark State Forest, Elk Creek Public Fishing Area, and Jackson-Washington State Forest. These state resource properties contain more than 42,000 acres of rugged, forested land in Clark, Scott and Washington counties in southern Indiana.
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
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The Lander Road departs the main trail at Burnt Ranch near South Pass, crosses the Continental Divide north of South Pass and reaches the Green River near the present town of Big Piney, Wyoming. From there the trail followed Big Piney Creek west before passing over the 8,800 feet (2,700 m) Thompson Pass in the Wyoming Range.