TY - JOUR

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

AU - Kakimura, Naonori

AU - Kawarabayashi, Ken ichi

N1 - Funding Information:
Supported by JST ERATO Grant Number JPMJER1201.
Publisher Copyright:
© 2018 Elsevier Inc.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/7

Y1 - 2018/7

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

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U2 - 10.1016/j.jctb.2018.02.003

DO - 10.1016/j.jctb.2018.02.003

M3 - Article

AN - SCOPUS:85042390871

VL - 131

SP - 138

EP - 169

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

ER -