Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  874.52010
Autor:  Erdös, Paul; Pach, János
Title:  Are there many distances that occur few times? (In English)
Source:  Geombinatorics 6, No.3, 77-78 (1997).
Review:  Let x1,...,xn be points in the plane and let {d1,...,dk} denote the different distances occurring between these points. It is known that the diameter D: = max di occurs at most n times. The authors conject that there is at least one other dj which occurs at most n times as well. They also state a conjecture concerning the sum of all the distances whose multiplicities are \leq n.
Reviewer:  B.Kind (Bochum)
Classif.:  * 52C10 Erdoes problems and related topics of discrete geometry
Keywords:  distances in finite planar sets

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag