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arXiv · 1802.05026

Directed cycles have the edge-Erd\H os-Pósa property

Matthias Heinlein·Arthur Ulmer
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Abstract

In this short note we prove that for every $k\in \mathbb{N}$ there is a $t_k\in\mathbb{N}$ such that for every digraph $G$ there are either $k$ edge-disjoint directed cycles in $G$ or a set $X$ of at most $t_k$ edges such that $G-X$ contains no directed cycle.

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Matthias Heinlein, Arthur Ulmer. 2018-02-14. Directed cycles have the edge-Erd\H os-Pósa property. https://arxiv.org/abs/1802.05026

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