The Edge-Erdős-Pósa Property


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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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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Correspondence to Henning Bruhn.

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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).

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Mathematics Subject Classification (2010)

  • 05B40