## 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: Tuesday, March 17, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Yves Brise

## Disjoint Covering Number

Consider the following setup: You are given a ground set of size $n$, i.e. $[n] := \{0, \ldots, n-1\}$, and two parameters $k$ and $r$, $1\leq r \leq k \leq n$. A $(n,k,r)$ covering $C$ is a set of $k$-subsets of $[n]$ such that ALL $r$-subsets of $[n]$ are contained in some member of $C$.

The problem of finding a covering of small size has already been well studied. Instead, we are interested in determining the maximum number of disjoint coverings. A set of coverings is called disjoint, if the coverings are pairwise disjoint, i.e. any pair of them does not use the same $k$-subset twice.

Joint work with Bernd Gärtner.

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