Problems related to a de Bruijn - Erd\H{o}s theorem
Combinatorics
2009-06-01 v1 Metric Geometry
Abstract
De Bruijn and Erd\H{o}s 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.
Cite
@article{arxiv.math/0610036,
title = {Problems related to a de Bruijn - Erd\H{o}s theorem},
author = {Xiaomin Chen and Vašek Chvátal},
journal= {arXiv preprint arXiv:math/0610036},
year = {2009}
}
Comments
11 pages. See also http://www.cs.concordia.ca/~chvatal/dbe.pdf