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arXiv · 2602.10340

Hunting for Directed 2-Spiders

Grzegorz Gutowski·Gaurav Kucheriya
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Abstract

Hons, Klimo\v{s}ov\'a, Kucheriya, Mik\v{s}an\'ik, 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.

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Grzegorz Gutowski, Gaurav Kucheriya. 2026-02-10. Hunting for Directed 2-Spiders. https://arxiv.org/abs/2602.10340

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