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The Edge-Erdős-Pósa Property

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Abstract

Robertson and Seymour proved that the family of all graphs containing a fixed graph H as a minor has the Erdős-Pósa property if and only if H is planar. We show that this is no longer true for the edge version of the Erdős-Pósa property, and indeed even fails when H is an arbitrary subcubic tree of large pathwidth or a long ladder. This answers a question of Raymond, Sau and Thilikos.

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Acknowledgement

We thank the anonymous referees for a very careful reading of the manuscript and many valuable comments that improved the manuscript.

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Authors and Affiliations

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

    Henning Bruhn & Matthias Heinlein

  2. Institut für Informatik, Universität Heidelberg, Heidelberg, Germany

    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 leading to these results was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 321904558.

The research leading to these results was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 339933727.

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Bruhn, H., Heinlein, M. & Joos, F. The Edge-Erdős-Pósa Property. Combinatorica 41, 147–173 (2021). https://doi.org/10.1007/s00493-020-4071-7

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  • DOI: https://doi.org/10.1007/s00493-020-4071-7

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