girth

The girth of a graph $G$ is the length of the shortest cycle in $G$.11There is no widespread agreement on the girth of a forest, which has no cycles. It is also extremely unimportant.

For instance, the girth of any grid $\mathbb{Z}^{d}$ (where $d>2$) is 4, and the girth of the vertex graph of the dodecahedron is 5.

Title girth Girth 2013-03-22 12:45:56 2013-03-22 12:45:56 ariels (338) ariels (338) 4 ariels (338) Definition msc 05C38 ChromaticNumberAndGirth