The edge-Erd\H{o}s-P\'osa property

Abstract

Robertson and Seymour proved that the family of all graphs containing a fixed graph $H$ as a minor has the Erd\H{o}s-P\'osa property if and only if $H$ is planar. We show that this is no longer true for the edge version of the Erd\H{o}s-P\'osa 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.