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A d-degree generalization of the Erdős-Ko-Rado Theorem

组织者

马杰 , 本杰明·苏达科夫

演讲者

Hao Huang

时间

2025年10月28日 17:05 至 18:15

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

Perhaps the most well-known theorem in extremal combinatorics, the Erdős-Ko-Rado (EKR) Theorem asserts that for n>=2k, an intersecting family of k-subsets of {1, ..., n} contains at most n-1 \choose k-1 sets. In 2017, Yi Zhao and I established a degree version of the EKR Theorem, showing that when n>=2k+1, the least popular element of the ground set is contained in at most n-2 \choose k-2 sets of such a family. In this talk, I will present a further generalization of these results to the setting of minimum d-degree, improving a result of Kupavskii. This is a joint work with Yi Zhang (BUPT).