Math 2.0

Combinatorics Definition

Trail

Builds on Walk

Definition

Let GG be a graph. A trail in GG is a walk (w0,w1,…,wk)(w_0, w_1, \dots, w_k) whose edges w0w1,w1w2,…,wk−1wkw_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 cc, the closed walk a,b,c,d,e,c,aa, b, c, d, e, c, a is a trail but not a path. An Eulerian trail is a trail that uses every edge.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph
Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionTrail, definition, no evidence levelTraildefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Trail definition

Where this leads

30 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Path_(graph_theory), Walk, trail, and path
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