Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, October 18, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

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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