In this short note we prove that for every k∈N there is a tk∈N such that for every digraph G there are either k edge-disjoint directed cycles in G or a set X of at most tk edges such that G−X contains no directed cycle.
@article{arxiv.1802.05026,
title = {Directed cycles have the edge-Erd\H os-P\'osa property},
author = {Matthias Heinlein and Arthur Ulmer},
journal= {arXiv preprint arXiv:1802.05026},
year = {2018}
}