The asymptotic version of the Erdős-Sós conjecture and beyond
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908897671905280 |
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| author | Davoodi, Akbar Piguet, Diana Řada, Hanka Sanhueza-Matamala, Nicolás |
| author_facet | Davoodi, Akbar Piguet, Diana Řada, Hanka Sanhueza-Matamala, Nicolás |
| contents | Klimošová, Piguet, and Rozhoň conjectured that any graph with minimum degree $k/2$ and sufficiently many vertices of degree $k$ should contain all trees with $k$ edges. We prove an asymptotic version of this conjecture for dense host graphs. We obtain interesting corollaries: the first is an asymptotic version of the Erdős--Sós conjecture for dense host graphs, which works without any bounded-degree restriction on the guest trees. Secondly, by leveraging recent results by Pokrovsky, we can translate our results to sparse host graphs in the case of bounded-degree guest trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17755 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The asymptotic version of the Erdős-Sós conjecture and beyond Davoodi, Akbar Piguet, Diana Řada, Hanka Sanhueza-Matamala, Nicolás Combinatorics 05C05, 05C35 Klimošová, Piguet, and Rozhoň conjectured that any graph with minimum degree $k/2$ and sufficiently many vertices of degree $k$ should contain all trees with $k$ edges. We prove an asymptotic version of this conjecture for dense host graphs. We obtain interesting corollaries: the first is an asymptotic version of the Erdős--Sós conjecture for dense host graphs, which works without any bounded-degree restriction on the guest trees. Secondly, by leveraging recent results by Pokrovsky, we can translate our results to sparse host graphs in the case of bounded-degree guest trees. |
| title | The asymptotic version of the Erdős-Sós conjecture and beyond |
| topic | Combinatorics 05C05, 05C35 |
| url | https://arxiv.org/abs/2603.17755 |