### Abstract

Let M be a representable matroid and Q,R, S, T subsets of the ground set such that the smallest separation that separates Q from R has order k, and the smallest separation that separates S from T has order l. We prove that if M is sufficiently large, then there is an element e such that in one of M\e and M/e both connectivities are preserved. For matroids representable over a finite field we prove a stronger result: we show that we can remove e such that both a connectivity and a minor of M are preserved.

Original language | English |
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Pages (from-to) | 188-196 |

Number of pages | 9 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

Externally published | Yes |

### Keywords

- Connectivity
- Intertwining
- Matroids
- Tutte s linking theorem

## Cite this

Huynh, T., & Van Zwam, S. H. M. (2014). Intertwining connectivities in representable matroids.

*SIAM Journal on Discrete Mathematics*,*28*(1), 188-196. https://doi.org/10.1137/13091837X