Intersecting families with covering number $3$
<|reference_start|>Intersecting families with covering number $3$: 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 $n>2k$.<|reference_end|>
@article{kupavskii2024intersecting,
    title={Intersecting families with covering number $3$},
    author={Andrey Kupavskii},
    journal={arXiv preprint arXiv:2405.02621},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02621},
    primaryClass={math.CO cs.DM}
}