The edge-Erdős-Pósa property
arXiv:1809.11038
Abstract
Robertson and Seymour proved that the family of all graphs containing a fixed graph as a minor has the Erdős-Pósa property if and only if is planar. We show that this is no longer true for the edge version of the Erdős-Pósa property, and indeed even fails when is an arbitrary subcubic tree of large pathwidth or a long ladder. This answers a question of Raymond, Sau and Thilikos.
22 pages