English

A De Bruijn-Erdos theorem for chordal graphs

Combinatorics 2021-10-26 v1

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 induced by connected chordal graphs.

Keywords

Cite

@article{arxiv.1201.6376,
  title  = {A De Bruijn-Erdos theorem for chordal graphs},
  author = {Laurent Beaudou and Adrian Bondy and Xiaomin Chen and Ehsan Chiniforooshan and Maria Chudnovsky and Vasek Chvatal and Nicolas Fraiman and Yori Zwols},
  journal= {arXiv preprint arXiv:1201.6376},
  year   = {2021}
}
R2 v1 2026-06-21T20:12:11.100Z