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A cycle in a graph, digraph, or multigraph, is a simple path from a vertex to itself (i.e., a path where the first vertex is the same as the last vertex and no edge is repeated).
For example, consider this graph:
 and  are two of the cycles in this graph.  is not a cycle, however, since it uses the edge connecting  and  twice.  is not a cycle because it begins on  but ends on  .
A cycle of length  is sometimes denoted  and may be referred to as a polygon of  sides: that is,  is a triangle,  is a quadrilateral,  is a pentagon, etc.
An even cycle is one of even length; similarly, an odd cycle is one of odd length.
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"cycle" is owned by mps. [ full author list (2) | owner history (1) ]
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(view preamble)
Cross-references: odd, even, pentagon, quadrilateral, triangle, sides, polygon, length, edge, path, vertex, simple path, multigraph, digraph, graph
There are 20 references to this entry.
This is version 5 of cycle, born on 2002-02-04, modified 2004-03-30.
Object id is 1805, canonical name is Cycle.
Accessed 4810 times total.
Classification:
| AMS MSC: | 05C38 (Combinatorics :: Graph theory :: Paths and cycles) |
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Pending Errata and Addenda
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