Abstract

Robertson and Seymour proved that the family of all graphs containing a fixed graph H as a minor has the Erdős-Posa property if and only if H is planar. We show that this is no longer true for the edge version of the Erdős-Posa 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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