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

Naonori Kakimura, Ken ichi Kawarabayashi

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
JournalJournal of Combinatorial Theory. Series B
DOIs
Publication statusAccepted/In press - 2018 Jan 1

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Immersion
Joining
Connected graph
Disjoint
Path
Edge-connectivity
Graph in graph theory
Packing
Pairwise
Distinct
Integer
Subset

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

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

In: Journal of Combinatorial Theory. Series B, 01.01.2018.

Research output: Contribution to journalArticle

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