• Czech: obvod
• French: circonférence
• German: Sattelgurt

The girth of an object is a measurement around it. It is sometimes used by postal services and delivery companies as a basis for pricing. For example, Canada Post requires that an item's length plus girth not exceed a maximum allowed value. For a rectangular box, the girth is 2 * (height + width), i.e. the perimeter of a cross section perpendicular to its length.

In graph theory, the girth of a graph is the length of the shortest cycle contained in the graph. If the graph does not 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. 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 triangle-free.

See also

• Systolic geometry

References

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