## 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, September 25, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Dominik Scheder

## Almost Disjoint Formulas and Almost Tight Bounds

Call a CNF formula *almost disjoint* if any two distinct clauses have at most one variable in common. What is the maximum integer m such that every almost disjoint k-CNF formula with m clauses is satisfiable? Denote this number by m(k). We prove pretty tight upper and lower bounds on m(k).

The upper bound uses a randomized construction of an unsatisfiable almost disjoint formula. We do not have any *explicit* construction that comes even close to the lower bound. However, we have certain arguments why a barehanded approach to constructing such formulas should always be difficult.

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