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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.08123 |
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| _version_ | 1866912954850476032 |
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| author | Gerbner, Dániel |
| author_facet | Gerbner, Dániel |
| contents | We say that a set system $\mathcal{F}$ is $k$-completely hyperseparating if for any vertex $v$, there are at most $k$ sets in $\mathcal{F}$ with intersection $\{v\}$. We determine the minimum size of such set systems on an $n$-element underlying set, generalizing a very recent result for $k=2$ by Batíková, Kepka, and Nemĕc.
We say that $\mathcal{F}$ is $k$-hyperseparating if for any vertex $v$, there are at most $k$ sets in $\mathcal{F}$ such that no other vertex is contained by exactly the same sets out of these $k$ sets. We determine the minimum size of $2$-hyperseparating set systems on an $n$-element underlying set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on hyperseparating set systems Gerbner, Dániel Combinatorics We say that a set system $\mathcal{F}$ is $k$-completely hyperseparating if for any vertex $v$, there are at most $k$ sets in $\mathcal{F}$ with intersection $\{v\}$. We determine the minimum size of such set systems on an $n$-element underlying set, generalizing a very recent result for $k=2$ by Batíková, Kepka, and Nemĕc. We say that $\mathcal{F}$ is $k$-hyperseparating if for any vertex $v$, there are at most $k$ sets in $\mathcal{F}$ such that no other vertex is contained by exactly the same sets out of these $k$ sets. We determine the minimum size of $2$-hyperseparating set systems on an $n$-element underlying set. |
| title | A note on hyperseparating set systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.08123 |