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Long Cycles have the Edge-Erdős-Pósa Property

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Abstract

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

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Authors and Affiliations

  1. Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany

    Henning Bruhn & Matthias Heinlein

  2. School of Mathematics, University of Birmingham, Birmingham, UK

    Felix Joos

Authors
  1. Henning Bruhn
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  2. Matthias Heinlein
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  3. Felix Joos
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Corresponding author

Correspondence to Henning Bruhn.

Additional information

The research was also supported by the EPSRC, grant no. EP/M009408/1.

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Bruhn, H., Heinlein, M. & Joos, F. Long Cycles have the Edge-Erdős-Pósa Property. Combinatorica 39, 1–36 (2019). https://doi.org/10.1007/s00493-017-3669-x

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  • DOI: https://doi.org/10.1007/s00493-017-3669-x

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