Long cycles have the edge-Erdős-Pósa property

We prove that the set of long cycles has the edge-Erdős-Pósa property: for every fixed integer ` ≥ 3 and every k ∈ N, every graph G either contains k edge-disjoint cycles of length at least ` (long cycles) or an edge set X of size O(k log k + `k) such that G−X does not contain any long cycle. This answers a question of Birmelé, Bondy, and Reed… (More)