Editing Girth (graph theory) (section)

== Related concepts ==
The '''odd girth''' and '''even girth''' of a graph are the lengths of a shortest odd cycle and shortest even cycle respectively. 

The '''{{visible anchor|circumference}}''' of a graph is the length of the ''longest'' (simple) cycle, rather than the shortest.

Thought of as the least length of a non-trivial cycle, the girth admits natural generalisations as the 1-systole or higher systoles in [[systolic geometry]].

Girth is the dual concept to [[k-edge-connected graph|edge connectivity]], in the sense that the girth of a [[planar graph]] is the edge connectivity of its [[dual graph]], and vice versa. These concepts are unified in [[matroid theory]] by the [[matroid girth|girth of a matroid]], the size of the smallest dependent set in the matroid. For a [[graphic matroid]], the matroid girth equals the girth of the underlying graph, while for a co-graphic matroid it equals the edge connectivity.<ref>{{citation
 | last1 = Cho | first1 = Jung Jin
 | last2 = Chen | first2 = Yong
 | last3 = Ding | first3 = Yu
 | doi = 10.1016/j.dam.2007.06.015
 | issue = 18
 | journal = Discrete Applied Mathematics
 | mr = 2365057
 | pages = 2456–2470
 | title = On the (co)girth of a connected matroid
 | volume = 155
 | year = 2007| doi-access = free
 }}.</ref>