### Abstract

Let κ be an infinite cardinal, and let H be either a complete graph with κ vertices, or a tree in which every vertex has valency κ. What can we say about graphs G which (i) have no minor isomorphic to H, or (ii) contain no subgraph which is a subdivision of H? These four questions are answered for each infinite cardinal κ. In each case we find that there corresponds a necessary and sufficient structural condition (or, in some cases, several equivalent conditions) for G not to contain H in the appropriate way. We survey these results and a number of related theorems.

Original language | English (US) |
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Pages (from-to) | 303-319 |

Number of pages | 17 |

Journal | Discrete Mathematics |

Volume | 95 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 3 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Robertson, N., Seymour, P., & Thomas, R. (1991). Excluding infinite minors.

*Discrete Mathematics*,*95*(1-3), 303-319. https://doi.org/10.1016/0012-365X(91)90343-Z