BIMSA >
Research seminar in Discrete Mathematics
A d-degree generalization of the Erdős-Ko-Rado Theorem
A d-degree generalization of the Erdős-Ko-Rado Theorem
Organizers
Jie Ma
, Benjamin Sudakov
Speaker
Hao Huang
Time
Tuesday, October 28, 2025 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
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).