The Brown-Erdős-Sós conjecture in dense triple systems
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913988632117248 |
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| author | Santos, Giovanne Tyomkyn, Mykhaylo |
| author_facet | Santos, Giovanne Tyomkyn, Mykhaylo |
| contents | The famous Brown-Erdős-Sós conjecture from 1973 states, in an equivalent form, that for any fixed $δ>0$ and integer $k\geq 3$ every sufficiently large linear $3$-uniform hypergraph of size $δn^2$ contains some $k$ edges spanning at most $k+3$ vertices. We prove it to hold for $δ>4/5$, establishing the first bound of this kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Brown-Erdős-Sós conjecture in dense triple systems Santos, Giovanne Tyomkyn, Mykhaylo Combinatorics The famous Brown-Erdős-Sós conjecture from 1973 states, in an equivalent form, that for any fixed $δ>0$ and integer $k\geq 3$ every sufficiently large linear $3$-uniform hypergraph of size $δn^2$ contains some $k$ edges spanning at most $k+3$ vertices. We prove it to hold for $δ>4/5$, establishing the first bound of this kind. |
| title | The Brown-Erdős-Sós conjecture in dense triple systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.09841 |