A De Bruijn-Erdos theorem for chordal graphs

Laurent Beaudou, Adrian Bondy, Xiaomin Chen, Ehsan Chiniforooshan, Maria Chudnovsky, Vasek Chvatal, Nicolas Fraiman, Yori Zwols

Published 2012-01-30Version 1

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 induced by connected chordal graphs.