# Half-integral Erd\H{o}s-P\'osa property of directed odd cycles

@article{Kawarabayashi2020HalfintegralEP, title={Half-integral Erd\H\{o\}s-P\'osa property of directed odd cycles}, author={Ken-ichi Kawarabayashi and Stephan Kreutzer and O-joung Kwon and Qiqin Xie}, journal={arXiv: Combinatorics}, year={2020} }

We prove that there exists a function $f:\mathbb{N}\rightarrow \mathbb{R}$ such that every digraph $G$ contains either $k$ directed odd cycles where every vertex of $G$ is contained in at most two of them, or a vertex set $X$ of size at most $f(k)$ hitting all directed odd cycles. This extends the half-integral Erdős-Posa property of undirected odd cycles, proved by Reed [Mangoes and blueberries. Combinatorica 1999], to digraphs.

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