Girth
From Wikipedia, the free encyclopedia
- A girth is also a piece of equipment used to hold the saddle on a horse.
Girth is 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 <math>g</math> that is as small as possible is known as a <math>g</math>-cage. 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. A graph with girth ≥ 4 is called triangle-free.
The Petersen graph, of girth 5 |
The Heawood graph, of girth 6 |
The Tutte eight cage, of girth 8 |
