A De Bruijn-Erdos theorem for 1-2 metric spaces

Abstract

A special case of a combinatorial theorem of De Bruijn and Erdos asserts 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 assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals 1 or 2.

References in corpus (1)

• A De Bruijn-Erdos theorem for chordal graphs

Cited by in corpus (3)

• The Chen-Chvátal conjecture for metric spaces induced by distance-hereditary graphs
• Number of lines in hypergraphs
• Lines, betweenness and metric spaces