@inproceedings{Masak2019PackingDC,
title={Packing directed circuits quarter-integrally},
author={Tom{\'a}{\vs} Masař{\'i}k and I. Muzi and Marcin Pilipczuk and Paweł Rzążewski and M. Sorge},
booktitle={ESA},
year={2019}
}

The celebrated Erdős-Posa theorem states that every undirected graph that does not admit a family of $k$ vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size $O(k \log k)$. After being known for long as Younger's conjecture, a similar statement for directed graphs has been proven in 1996 by Reed, Robertson, Seymour, and Thomas. However, in their proof, the dependency of the size of the feedback vertex set on the size of vertex… CONTINUE READING