Hunting for Directed 2-Spiders
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Gutowski, Grzegorz Kucheriya, Gaurav |
| author_facet | Gutowski, Grzegorz Kucheriya, Gaurav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hunting for Directed 2-Spiders Gutowski, Grzegorz Kucheriya, Gaurav Combinatorics 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. |
| title | Hunting for Directed 2-Spiders |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.10340 |