### Abstract

A graph H is immersed in a graph G if the vertices of H are mapped to distinct vertices of G, and the edges of H are mapped to paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. In this paper, we show that the Erdős–Pósa property holds for packing edge-disjoint K_{t}-immersions in 4-edge-connected graphs. More precisely, for positive integers k and t, there exists a constant f(k,t) such that a 4-edge-connected graph G has either k edge-disjoint K_{t}-immersions, or an edge subset F of size at most f(k,t) such that G−F has no K_{t}-immersion. The 4-edge-connectivity in this statement is best possible in the sense that 3-edge-connected graphs do not have the Erdős–Pósa property.

Original language | English |
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Pages (from-to) | 138-169 |

Number of pages | 32 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 131 |

DOIs | |

Publication status | Published - 2018 Jul |

### Keywords

- 4-Edge-connected graphs
- Covering
- Immersion
- Packing

### ASJC Scopus subject areas

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

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## Cite this

*Journal of Combinatorial Theory. Series B*,

*131*, 138-169. https://doi.org/10.1016/j.jctb.2018.02.003