Vipul: Created page with "{{undirected graph numerical invariant}} ==Definition== The '''odd girth''' of an undirected graph is defined as the minimum of the lengths of cycles of odd length (i.e...."

2012-05-29T02:38:25Z

Created page with "{{undirected graph numerical invariant}} ==Definition== The '''odd girth''' of an undirected graph is defined as the minimum of the lengths of cycles of odd length (i.e...."

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{{undirected graph numerical invariant}}

==Definition==

The '''odd girth''' of an [[undirected graph]] is defined as the minimum of the lengths of cycles of odd length (i.e., subgraphs that are isomorphic to [[cycle graph]]s). The odd girth is taken to be <math>\infty</math> if there is no cycle of odd length.

==Particular cases==

{| class="sortable" border="1"
! Value of odd girth !! What it tells us about the graph
|-
| <math>\infty</math> || There are no cycles of odd length. Equivalently, the graph is a [[bipartite graph]].
|-
| strictly greater than 3, i.e., at least 5 || The graph is a [[triangle-free graph]].
|}

==Related invariants==

* [[Girth]] refers to the minimum of the lengths of all cycles, whether even or odd.
* [[Even girth]] refers to the minimum of the lengths of all cycles of even length.

Odd girth - Revision history

Vipul: Created page with "{{undirected graph numerical invariant}} ==Definition== The '''odd girth''' of an undirected graph is defined as the minimum of the lengths of cycles of odd length (i.e...."