Problems related to a de Bruijn - Erdős theorem
arXiv:math/0610036
Abstract
De Bruijn and Erdős proved that every noncollinear set of n points in the plane determines at least n distinct lines. We suggest a possible generalization of this theorem in the framework of metric spaces and provide partial results on related extremal combinatorial problems.
11 pages. See also http://www.cs.concordia.ca/~chvatal/dbe.pdf