PhD seminar: The union-closed sets conjecture
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Johanna Strömberg
- Contact person: Volodymyr Mazorchuk
A family of sets is said to be union-closed if the union of any two sets in the family is in the family. The conjecture, first posed by Frankl in 1979, states that for any finite union-closed family of finite sets there is one element belonging to at least half the sets.There are equivalent formulations in terms of lattices and graphs and a number of partial results, but no proof. An elementary result is that if one set in the family has size two, the conjecture is known to be true. In this talk we explore some of the partial results, in particular related to the graph theory reformulation of the conjecture.