### 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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Journal | Journal of Combinatorial Theory. Series B |

DOIs | |

Publication status | Accepted/In press - 2018 Jan 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Combinatorial Theory. Series B*. https://doi.org/10.1016/j.jctb.2018.02.003

**The Erdős–Pósa property for edge-disjoint immersions in 4-edge-connected graphs.** / Kakimura, Naonori; Kawarabayashi, Ken ichi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The Erdős–Pósa property for edge-disjoint immersions in 4-edge-connected graphs

AU - Kakimura, Naonori

AU - Kawarabayashi, Ken ichi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 Kt-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 Kt-immersions, or an edge subset F of size at most f(k,t) such that G−F has no Kt-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.

AB - 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 Kt-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 Kt-immersions, or an edge subset F of size at most f(k,t) such that G−F has no Kt-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.

KW - 4-Edge-connected graphs

KW - Covering

KW - Immersion

KW - Packing

UR - http://www.scopus.com/inward/record.url?scp=85042390871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042390871&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2018.02.003

DO - 10.1016/j.jctb.2018.02.003

M3 - Article

AN - SCOPUS:85042390871

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

ER -