## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, November 09, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Uli Wagner

## Set pairs (and, time permitting, quadrupels)

This will be, for the most part, an expository talk about (variants of) an extremal problem about finite sets, some results (key words Bollobás's Theorem'' and its skew version'') and some applications.

The focus will be on the proof methods.

Time permitting, we will also mention some recent generalizations.

If you are curious, the basic version of the problem is this: Suppose we are given some unknown number $t$ of pairs $(A_i,B_i)$ of finite sets, $1 \leq i \leq t$ with the following constraints:

0) $|A_i| \leq a$ and $|B_i| \leq b$ for all $i$, for some constants $a,b$;
1) $A_i \cap B_i = \emptyset$ for all $i$;
2) $A_i \cap B_j eq \emptyset$ for $i eq j$.

Bollobás showed that the number of pairs is at most $\binom{a+b}{a}$.

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