Math 2.0

Combinatorics Definition

Circuit

Builds on Trail

Definition

Let GG be a graph. A circuit in GG is a closed trail of positive length. That is a walk (w0,w1,…,wk)(w_0, w_1, \dots, w_k) with k≥1k \ge 1, wk=w0w_k = w_0, and pairwise distinct edges.

Remarks

A circuit may visit a vertex more than once. A cycle is a circuit with no repeated vertex other than the start. In a simple graph each circuit has length at least 33. Some authors use the word circuit for a cycle. Others use the word tour.

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 levelTraildefinitionCircuit, definition, no evidence levelCircuitdefinition
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. Circuit definition

Where this leads

26 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Cycle_(graph_theory), Circuit and cycle
About this page
Tag0PD57PSHNR
URIm2://0PD57PSHNR
Kinddefinition
WritingW0 stub
MSC05C38
DefinesCircuit
UsesTrail

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (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