Proof of the KAMAK tree conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908381602643968 |
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| author | Christoph, Micha Steiner, Raphael |
| author_facet | Christoph, Micha Steiner, Raphael |
| contents | There are many intriguing questions in extremal graph theory that are well-understood in the undirected setting and yet remain elusive for digraphs. A natural instance of such a problem was recently studied by Hons, Klimošová, Kucheriya, Mikšaník, Tkadlec and Tyomkyn: What are the digraphs that have to appear as a subgraph in all digraphs of sufficiently large minimum out-degree? Hons et al. showed that all such digraphs must be oriented forests with a specific structure, and conjectured that vice-versa all oriented forests with this specific structure appear in any digraph of sufficiently large minimum out-degree. In this paper, we confirm their conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof of the KAMAK tree conjecture Christoph, Micha Steiner, Raphael Combinatorics There are many intriguing questions in extremal graph theory that are well-understood in the undirected setting and yet remain elusive for digraphs. A natural instance of such a problem was recently studied by Hons, Klimošová, Kucheriya, Mikšaník, Tkadlec and Tyomkyn: What are the digraphs that have to appear as a subgraph in all digraphs of sufficiently large minimum out-degree? Hons et al. showed that all such digraphs must be oriented forests with a specific structure, and conjectured that vice-versa all oriented forests with this specific structure appear in any digraph of sufficiently large minimum out-degree. In this paper, we confirm their conjecture. |
| title | Proof of the KAMAK tree conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.21367 |