Intersecting families with covering number $3$
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911284046331904 |
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| author | Kupavskii, Andrey |
| author_facet | Kupavskii, Andrey |
| contents | A covering number of a family is the size of the smallest set that intersects all sets from the family. In 1978 Frankl determined for $n\ge n_0(k)$ the largest intersecting family of $k$-element subsets of $[n]$ with covering number $3$. In this paper, we essentially settle this problem, showing that the same family is extremal for any $k\ge 100$ and $n>2k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersecting families with covering number $3$ Kupavskii, Andrey Combinatorics Discrete Mathematics A covering number of a family is the size of the smallest set that intersects all sets from the family. In 1978 Frankl determined for $n\ge n_0(k)$ the largest intersecting family of $k$-element subsets of $[n]$ with covering number $3$. In this paper, we essentially settle this problem, showing that the same family is extremal for any $k\ge 100$ and $n>2k$. |
| title | Intersecting families with covering number $3$ |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2405.02621 |