# girth

The *girth* of a graph $G$ is the length of the shortest cycle in $G$.^{1}^{1}There 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 |
---|---|

Canonical name | Girth |

Date of creation | 2013-03-22 12:45:56 |

Last modified on | 2013-03-22 12:45:56 |

Owner | ariels (338) |

Last modified by | ariels (338) |

Numerical id | 4 |

Author | ariels (338) |

Entry type | Definition |

Classification | msc 05C38 |

Related topic | ChromaticNumberAndGirth |