Combinatorics Seminar
When: Sunday, December 23, 10am
Where: Schreiber 309
Speaker: Benny Sudakov, University of California at Los
Angeles
Title: Maximum union-free subfamilies
Abstract:
A family of sets is called union-free if there are no three distinct
sets in the family such that the union of two of the sets is equal
to the third set. An old problem of Moser asks: how large of
a union-free subfamily does every family of m sets have? In this talk
I will prove that every family of m sets contains a union-free
subfamily of size at least [\sqrt{4m+1}]- 1 and that this bound is
tight for all m. This solves Moser's problem and proves in a strong
form a conjecture of Erdos and Shelah from 1972. I will also discuss
some related results and open problems.
Joint work with Jacob Fox and Choongbum Lee.