### Abstract

Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is a set of vertices of cardinality k that cannot be separated from the tangle by any separation of order less than k, then G has a large grid minor containing Z, in which the members of Z all belong to the outside of the grid.

Original language | English (US) |
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Pages (from-to) | 428-437 |

Number of pages | 10 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 122 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

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

### Keywords

- Grid minors
- Tangles
- Treewidth

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## Cite this

Marx, D., Seymour, P., & Wollan, P. (2017). Rooted grid minors.

*Journal of Combinatorial Theory. Series B*,*122*, 428-437. https://doi.org/10.1016/j.jctb.2016.07.003