## 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, October 18, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Andreas Razen

## Transforming Perfect Matchings

For a planar point set we consider the graph of crossing-free straight-line perfect matchings where two perfect matchings are adjacent if their union is crossing-free. In 2005 Houle et al. showed that this graph is connected and gave an upper bound of $n-2$ for its diameter, $n$ being the number of given points. Recently, this upper bound was improved to $O(log n)$ by Aichholzer et al.

We prove a lower bound of $\Omega( log n / log log n )$ for the diameter of this graph. So far only constant lower bounds were known.

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