A de Bruijn - Erd\H{o}s theorem and metric spaces
Combinatorics
2012-05-08 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. Chen and Chv\'atal suggested a possible generalization of this theorem in the framework of metric spaces. We provide partial results in this direction.
Cite
@article{arxiv.0906.0123,
title = {A de Bruijn - Erd\H{o}s theorem and metric spaces},
author = {Ehsan Chiniforooshan and Vašek Chvátal},
journal= {arXiv preprint arXiv:0906.0123},
year = {2012}
}