On the Diameter of Sets with Maximum Number of Unit Distances

Peter Braß
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin, Germany
email: brass@inf.fu-berlin.de

Report B 98-02
February 1998

The problem of the maximum number of unit distances among n points in the plane is a famous unsolved problem of Paul Erdös. In this paper, we determine some structural information on the extremal sets. We show that the diameter of the extremal sets is not much bigger than the unit distance, so there are many distances smaller than one in a set with maximum number of unit distances.

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