# subdivision

A graph $H$ is said to be a *subdivision*, or *topological minor* of a graph $G$, or a *topological $G$ graph* if $H$ is obtained from $G$ by subdividing some of the edges, that is, by replacing the edges by paths having at most their endvertices in common. We often use $TG$ for a topological $G$ graph.

Thus, $TG$ denotes *any* member of a large family of graphs; for example, $T{C}_{4}$ is an arbitrary cycle of length at least 4. For any graph $G$, the spaces $R(G)$ (denoting the realization of G) and $R(TG)$ are homeomorphic.

Adapted with permission of the author from by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Title | subdivision |
---|---|

Canonical name | Subdivision |

Date of creation | 2013-03-22 12:31:51 |

Last modified on | 2013-03-22 12:31:51 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 5 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 05C99 |

Synonym | topological minor |

Related topic | Homeomorphic |

Related topic | Realization |