Cycles - Revision history

Admin: /* Graphs */

2019-04-26T22:28:25Z

Graphs

← Older revision		Revision as of 22:28, 26 April 2019
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	An ''Euler Cycle'' is slightly more restrictive - it is a path through the graph that visits every edge of the graph exactly once, '''and''' it starts and ends on the same node of the graph.		An ''Euler Cycle'' is slightly more restrictive - it is a path through the graph that visits every edge of the graph exactly once, '''and''' it starts and ends on the same node of the graph.

			==Finding Cycles on a Directed Graph==

			===Conditions===

			For an Euler Cycle to exist on a graph, the following must be true:

			1. All vertices with nonzero degree belong to a single strongly connected component.

			2. In degree and out degree of every vertex is same.

			If these conditions are met, we can use the Kosaraju algorithm to find the Euler cycle.

			===Kosaraju Pseudocode for Finding Connected Components===

			{{Main\|Graphs/Connected Components}}

			The Kosaraju algorithm is an algorithm for finding connected components on a graph.

	==Related==		==Related==

Admin: /* Graphs */

2019-04-26T22:09:21Z

Graphs

← Older revision		Revision as of 22:09, 26 April 2019
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	===Graphs===		===Graphs===

	On a graph, an Euler ~~Cycle~~ is a path through the graph that traverses every edge of the graph exactly once.		On a graph, an '''Euler Path''' is a path through the graph that traverses every edge of the graph exactly once.


			An ''Euler Cycle'' is slightly more restrictive - it is a path through the graph that visits every edge of the graph exactly once, '''and''' it starts and ends on the same node of the graph.

	==Related==		==Related==

Admin at 22:06, 26 April 2019

2019-04-26T22:06:26Z

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-A cycle is an important concept to [[Permutations]] and [[Combinatorics]].
+==What is a cycle==
 ==Related==
 * [[Inversions]]

Admin: /* Flags */

2019-03-27T01:20:38Z

Flags

← Older revision		Revision as of 01:20, 27 March 2019
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	{{CombinatoricsFlag}}		{{CombinatoricsFlag}}

			{{AOCPFlag}}

Admin: Created page with "A cycle is an important concept to Permutations and Combinatorics. A cycle is a way of writing a unique permutation in a unique way. (Permutations can also be written..."

2019-03-27T00:14:00Z

Created page with "A cycle is an important concept to Permutations and Combinatorics. A cycle is a way of writing a unique permutation in a unique way. (Permutations can also be written..."

New page

A cycle is an important concept to [[Permutations]] and [[Combinatorics]].

A cycle is a way of writing a unique permutation in a unique way. (Permutations can also be written using two-line notation, where the first row consists of all items in their natural order, and the second row consists of the items in the order specified by the permutation, but the two-row representation is not unique.)

==Related==

* [[Inversions]]
* [[Permutations]]
* [[Rubiks Cube/Permutations]]
* [[Combinatorics]]

==Flags==

{{CombinatoricsFlag}}