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

Naonori Kakimura, Ken ichi Kawarabayashi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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
Pages (from-to)138-169
Number of pages32
JournalJournal of Combinatorial Theory. Series B
Volume131
DOIs
Publication statusPublished - 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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