A girth is also a piece of equipment used to hold the saddle on a horse.

Girth generally refers to the circumference of a cylindrical object, such as a tree trunk.

Girth is sometimes used by postal services and delivery companies as basis for pricing. For example (for at least one delivery company), if you have a box to ship, it has three sides: length (the longest side) and height and width. The girth in this case is 2 * (height + width).

In graph theory, the girth of a graph is the length of the shortest cycle contained in the graph. If the graph doesn't contain any cycles, its girth is defined to be infinity.

For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.

A cubic graph of girth $g$ that is as small as possible is known as a $g$-cage graph. The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5). The Heawood graph is the unique 6-cage, and the Tutte eight cage is the unique 8-cage.

Image:Petersen graph.svg|The Petersen graph, of girth 5 Image:Heawood graph.svg|The Heawood graph, of girth 6 Image:Tutte eight cage.svg|The Tutte eight cage, of girth 8

Graph theory

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