A de Bruijn - Erdos theorem and metric spaces

Ehsan Chiniforooshan (1) , Vasek Chvatal (2)

1 Google Inc.
2 CSE - Department of Computer Science and Software Engineering [Montreal]

De Bruijn and Erdos proved that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this theorem in the framework of metric spaces. We provide partial results in this direction.

Domaines: Mathématique discrète [cs.DM]

Ehsan Chiniforooshan, Vasek Chvatal. A de Bruijn - Erdos theorem and metric spaces. Discrete Mathematics and Theoretical Computer Science, 2011, Vol. 13 no. 1 (1), pp.67--74. ⟨10.46298/dmtcs.545⟩. ⟨hal-00990496⟩