### Abstract

For each infinite cardinal k we give several necessary and sufficient conditions for a graph not to contain a minor isomorphic to the infinite k-branching tree in terms of a certain kind of a “tree-decomposition,” in terms of a “path-decomposition,” and alsoin terms of a “cops-and-robber game.” We also give necessary and sufficient conditions for a graph not to contain a subgraph isomorphic to a subdivision of the same tree.

Original language | English (US) |
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Pages (from-to) | 597-630 |

Number of pages | 34 |

Journal | Transactions of the American Mathematical Society |

Volume | 335 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1993 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Seymour, P. D., & Thomas, R. (1993). Excluding infinite trees.

*Transactions of the American Mathematical Society*,*335*(2), 597-630. https://doi.org/10.1090/S0002-9947-1993-1079058-6