论文标题
大型超级杂物的定向循环
Oriented cycles in digraphs of large outdegree
论文作者
论文摘要
1985年，Mader推测，对于每个无环的Digraph $ f $，存在$ k = k（f）$，使每个digraph $ d $具有最低级别的均值至少$ k $都包含$ f $的细分。即使对于五个顶点的Digraphs $ f $，这个猜想仍然是广泛开放的。 Recently, Aboulker, Cohen, Havet, Lochet, Moura and Thomassé studied special cases of Mader's problem and made the following conjecture: for every $\ell \geq 2$ there exists $K = K(\ell)$ such that every digraph $D$ with minimum out-degree at least $K$ contains a subdivision of every orientation of a cycle of length $\ell$.我们证明了这种猜想，并回答了Aboulker等人提出的进一步的开放问题。
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 $\ell \geq 2$ there exists $K = K(\ell)$ such that every digraph $D$ with minimum out-degree at least $K$ contains a subdivision of every orientation of a cycle of length $\ell$. We prove this conjecture and answer further open questions raised by Aboulker et al.
