### Abstract

Let Wt denote the wheel on t + 1 vertices. We prove that for every integer t ≥ 3 there is a constant c = c(t) such that for every integer k ≥ 1 and every graph G, either G has k vertex-disjoint subgraphs each containing Wt as a minor, or there is a subset X of at most ck log k vertices such that G - X has no Wt minor. This is best possible, up to the value of c. We conjecture that the result remains true more generally if we replace Wt with any fixed planar graph H.

Original language | English |
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Pages (from-to) | 2302-2312 |

Number of pages | 11 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 32 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Externally published | Yes |

### Keywords

- Covering
- Erdos--Pósa property
- Packing
- Wheel minors

## Cite this

Aboulker, P., Fiorini, S., Huynh, T., Joret, G., Raymond, J. F., & Sau, I. (2018). A tight Erdős–Pósa function for wheel minors.

*SIAM Journal on Discrete Mathematics*,*32*(3), 2302-2312. https://doi.org/10.1137/17M1153169