Math 2.0

Combinatorics Definition

Eulerian trail

Builds on Trail

Definition

Let GG be a graph or a multigraph. An Eulerian trail of GG is a trail in GG that uses every edge of GG exactly once. An Eulerian circuit is an Eulerian trail that starts and ends at the same vertex.

Remarks

A graph with an Eulerian circuit is called Eulerian. Euler's theorem characterizes the connected graphs with an Eulerian circuit by the parity of the degrees. The Seven Bridges of Königsberg form a multigraph with no Eulerian trail.

Reading path

To understand this page from the ground up, read these 4 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 levelTraildefinitionEulerian trail, definition, no evidence levelEulerian traildefinition
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
  4. Eulerian trail definition

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Eulerian_path, Definition
About this page
Tag0NNYDD1AVR
URIm2://0NNYDD1AVR
Kinddefinition
WritingW1 stated
MSC05C45
DefinesEulerian trail
UsesTrail

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by