# Ore’s theorem

Let $G$ be a simple graph^{} of order $n\ge 3$ such that, for every pair of distinct non adjacent vertices $u$ and $v$, $\mathrm{deg}(u)+\mathrm{deg}(v)\ge n$.
Then $G$ is a Hamiltonian graph^{}.

Title | Ore’s theorem |
---|---|

Canonical name | OresTheorem |

Date of creation | 2013-03-22 11:52:40 |

Last modified on | 2013-03-22 11:52:40 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 10 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 05C45 |

Classification | msc 18D20 |

Related topic | HamiltonianGraph |

Related topic | BondyAndChvatalTheorem |