# Wagner’s theorem

###### Theorem 1 (Wagner)

A graph is planar if and only if it contains neither ${K}_{\mathrm{5}}$ nor ${K}_{\mathrm{3}\mathrm{,}\mathrm{3}}$ as a minor, where ${K}_{\mathrm{5}}$ is the complete graph^{} of order 5 and ${K}_{\mathrm{3}\mathrm{,}\mathrm{3}}$ is the complete bipartite graph^{} of order 6.

Wagner’s theorem is to Kuratowski’s theorem.

Title | Wagner’s theorem |
---|---|

Canonical name | WagnersTheorem |

Date of creation | 2013-03-22 12:31:49 |

Last modified on | 2013-03-22 12:31:49 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 7 |

Author | Mathprof (13753) |

Entry type | Theorem |

Classification | msc 05C99 |

Related topic | PlanarGraph |

Related topic | KuratowskisTheorem |