### Abstract

Fix g > 1. Every graph of large enough tree-width contains a g× g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g× g grid as an immersion (and hence contains any fixed graph with maximum degree at most four as an immersion). This result has a number of applications.

Original language | English (US) |
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Pages (from-to) | 208-218 |

Number of pages | 11 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 116 |

DOIs | |

State | Published - Jan 2016 |

### All Science Journal Classification (ASJC) codes

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

### Keywords

- Graph immersion
- Grid minors

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## Cite this

Chudnovsky, M., Dvořák, Z., Klimošová, T., & Seymour, P. (2016). Immersion in four-edge-connected graphs.

*Journal of Combinatorial Theory. Series B*,*116*, 208-218. https://doi.org/10.1016/j.jctb.2015.07.006