# equivalence between the minor and topological minor of ${K}_{5}$ or ${K}_{3,3}$

A graph $G$ contains ${K}_{5}$ or ${K}_{3,3}$ as a minor iff it contains ${K}_{5}$ or ${K}_{3,3}$ as a topological minor (http://planetmath.org/subdivision). Where ${K}_{5}$ is the complete graph^{} of order 5 and ${K}_{3,3}$ is the complete bipartite graph^{} of order 6.

Remark that this theorem shows that Wagner’s theorem and Kuratowski’s theorem are equivalent^{}.

Title | equivalence between the minor and topological minor of ${K}_{5}$ or ${K}_{3,3}$ |
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Canonical name | EquivalenceBetweenTheMinorAndTopologicalMinorOfK5OrK33 |

Date of creation | 2013-03-22 17:47:13 |

Last modified on | 2013-03-22 17:47:13 |

Owner | jwaixs (18148) |

Last modified by | jwaixs (18148) |

Numerical id | 8 |

Author | jwaixs (18148) |

Entry type | Theorem |

Classification | msc 05C83 |

Classification | msc 05C10 |