Editing Girth (graph theory) (section)

{{short description|Length of a shortest cycle contained in the graph}}
In [[graph theory]], the '''girth''' of an [[undirected graph]] is the length of a shortest [[Cycle (graph theory)|cycle]] contained in the graph.<ref>R. Diestel, ''Graph Theory'', p.8.  3rd Edition, Springer-Verlag, 2005</ref> If the graph does not contain any cycles (that is, it is a [[forest (graph theory)|forest]]), its girth is defined to be [[infinity]].<ref>{{mathworld|id=Girth|title=Girth|mode=cs2}}</ref>
For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph with girth four or more is [[triangle-free graph|triangle-free]].