In 1985, Mader conjectured that for every acyclic digraph F there exists K = K(F) such that every digraph D with minimum out-degree at least K contains a subdivision of F. This conjecture remains widely open, even for digraphs F on five vertices. Recently, Aboulker, Cohen, Havet, Lochet, Moura and Thomassé studied special cases of Mader’s problem and made the following conjecture: for every ℓ ≥ 2 there exists K = K(ℓ) such that every digraph D with minimum out-degree at least K contains a subdivision of every orientation of a cycle of length ℓ.

We prove this conjecture and answer further open questions raised by Aboulker et al.

1985 年，Mader 猜想对于每个无环有向图F存在K = K ( F ) 使得每个具有最小出度至少K的有向图D都包含F的一个细分。这个猜想仍然广泛开放，即使对于五个顶点上的有向图F也是如此。最近，Aboulker、Cohen、Havet、Lochet、Moura 和 Thomassé 研究了 Mader 问题的特殊情况，并提出以下猜想：对于每ℓ ≥ 2，存在 K = K ( ℓ ) 使得每个有向图D至少具有最小出度ķ包含长度为ℓ的循环的每个方向的细分。

我们证明了这一猜想并回答了 Aboulker 等人提出的进一步的开放性问题。