摘要
The celebrated Erdős–Ko–Rado theorem determines the maximum size of a k-uniform intersecting family. The Hilton–Milner theorem determines the maximum size of a k-uniform intersecting family that is not a subfamily of the so-called Erdős–Ko–Rado family. In turn, it is natural to ask what the maximum size of an intersecting k-uniform family that is neither a subfamily of the Erdős–Ko–Rado family nor of the Hilton–Milner family is. For k ≥ 4, this was solved (implicitly) in the same paper by Hilton–Milner in 1967. We give a different and simpler proof, based on the shifting method, which allows us to solve all cases k ≥ 3 and characterize all extremal families achieving the extremal value.
源语言 | 英语 |
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页(从-至) | 73-87 |
页数 | 15 |
期刊 | Proceedings of the American Mathematical Society |
卷 | 145 |
期 | 1 |
DOI | |
出版状态 | 已出版 - 2017 |
已对外发布 | 是 |
指纹
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Han, J., & Kohayakawa, Y. (2017). The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton–Milner family. Proceedings of the American Mathematical Society, 145(1), 73-87. https://doi.org/10.1090/proc/13221