Author(s)

Amir Jafari, Amin Najafi Amin

Department of Mathematics, Sharif University of Technology, Tehran, Iran.

ErdÖs asks if it is possible to have n points in general position in the plane (no three on a line or four on a circle) such that for every i (1≤i≤n-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2≤n≤8 [1] [2]. A solution for the 8 point is provided by I. Palasti [3]. Here two other possible solutions for the 8 point case as well as all possible answers to 4 - 7 point cases are provided and finally a brief discussion on the generalization of the problem to higher dimensions is given.

ErdÖs Distance Problem, General Position, Graph Pattern, Distance Distribution

Jafari, A. and Amin, A. (2016) On the ErdÖs Distance Conjecture in Geometry. Open Journal of Discrete Mathematics, 6, 109-160. doi: 10.4236/ojdm.2016.63012.