寻找有向2-蜘蛛
Hunting for Directed 2-Spiders
AI总结：
本文证明了每个最小出度至少为2ℓ的有向图都包含一个(2,ℓ)-蜘蛛作为子图，改进了之前关于有向图中蜘蛛结构的结论。
摘要：
霍恩斯、克里莫索娃、库切里亚、米克沙尼克、塔达莱茨和托伊姆金证明，对于每一个整数ℓ≥1，每个最小出度至少为3.23·ℓ的有向图都包含一个(2,ℓ)-蜘蛛（一个具有ℓ个叶子的1-子分割的入星）作为子图。他们还猜想，最小出度的界限可以进一步改进到2ℓ。在本笔记中，我们通过证明每个最小出度至少为2ℓ的有向图都包含一个(2,ℓ)-蜘蛛作为子图来确认这一猜想。这个结果是最佳的，因为具有2ℓ个顶点的完全有向图不包含一个(2,ℓ)-蜘蛛。
英文摘要：
Hons, Klimošová, Kucheriya, Mikšaník, Tkadlec, and Tyomkyn proved that, for every integer $\ell \ge 1$, every directed graph with minimum out-degree at least $3.23 \cdot \ell$ contains a $(2,\ell)$-spider (a $1$-subdivision of the in-star with $\ell$ leaves) as a subgraph. They also conjectured that the bound on the minimum out-degree can be further improved to $2 \ell$. In this note, we confirm their conjecture by showing that every directed graph with minimum out-degree at least $2\ell$ contains a $(2, \ell)$-spider as a subgraph. This result is best possible, as the complete directed graph with $2\ell$ vertices does not contain a $(2,\ell)$-spider.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
