Füredi Zoltán: A useful tool in combinatorics: Intersecting set-pair systems (newest results with A. Gyárfás and Z. Király)

Abstract:

A {cross intersecting set pair system} (SPS) is:   (A_i, B_i) {i=1}^m
A_i\cap B_i=\emptyset and A_i\cap B_j\ne\emptyset.
It is an important tool of extremal combinatorics. Bollobás'
 classical result states that m\le {a+b\choose a} if
|A_i|\le a and |B_i|\le b for each i.

Our central {\problem} is to see how this bound changes with additional conditions.

{1-cross intersecting} set pair system: |A_i\cap B_j|=1 for all i\ne j.
We show connections to {perfect graphs}, clique partitions of graphs, and {finite geometries}.
Many problems are proposed.

Zoom link:
https://zoom.us/j/97677600671?pwd=ZlBIQU1ZTkRKcFhzTmdtdmUvYlFldz09