Leírás
The next lecture in the Extremal seminar will be on November 7 at 12:30 in the Nagyterem of the Rényi Institute.
Speaker: Joanna Jasińska
Title: On the number of disjoint pairs in a uniform family
Abstract
The famous theorem of Erdős--Ko--Rado states that the maximal size of an intersecting family of $k$-element subsets of $[n]$ is $\binom{n-1}{k-1}$, if $k \leqslant \frac{n}{2}$. In this talk, I will present the results from joint work with Gyula Katona, where we study the number of disjoint pairs of sets in a family of size greater than this. We provide a bound on the number of disjoint pairs depending on the size of minimum vertex cover of the graph representation of the family. I will present a new, elementary proof for a special case of a theorem of Dan, Gas and Sudakov, which claims that the minimal number of disjoint pairs of sets in set systems of size greater than $\binom{n-1}{k-1}$ can be obtained by considering families consisting of the initial segment of lexicographical order.
ZOOM
Meeting ID 825 2991 8779
Passcode 791691
https://us06web.zoom.us/j/82529918779?pwd=WtyNBEuyAuq4Lq2akfHHSY0aOR9VVm.1