### Abstract

We prove that for any infinite set of graphs of bounded genus, some member of the set is isomorphic to a minor of another. As a consequence, for any surface Σ there is a finite list of graphs, such that a general graph may be drawn in Σ if an only if it topologically contains none of the graphs in the list.

Original language | English (US) |
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Pages (from-to) | 255-288 |

Number of pages | 34 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1990 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Robertson, N., & Seymour, P. D. (1990). Graph minors. VIII. A kuratowski theorem for general surfaces.

*Journal of Combinatorial Theory, Series B*,*48*(2), 255-288. https://doi.org/10.1016/0095-8956(90)90121-F