, Volume 39, Issue 1, pp 1–36 | Cite as

Long Cycles have the Edge-Erdős-Pósa Property

  • Henning BruhnEmail author
  • Matthias Heinlein
  • Felix Joos


We prove that the set of long cycles has the edge-Erdős-Pósa property: for every fixed integer ≥ 3 and every k ∈ ℕ, every graph G either contains k edge-disjoint cycles of length at least (long cycles) or an edge set X of size O(k2 logk+kℓ) such that GX does not contain any long cycle. This answers a question of Birmelé, Bondy, and Reed (Combinatorica 27 (2007), 135-145).

Mathematics Subject Classification (2010)



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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2018

Authors and Affiliations

  1. 1.Institut für Optimierung und Operations ResearchUniversität UlmUlmGermany
  2. 2.School of MathematicsUniversity of BirminghamBirminghamUK

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