A de Bruijn-Erdős theorem for chordal graphs (Q2341062)

Summary: A special case of a combinatorial theorem of \textit{N. G. De Bruijn} and \textit{P. Erdős} [``On a combinatorial problem'', Indagationes Mathematicae 10, 421--423 (1948)] asserts that every noncollinear set of \(n\) points in the plane determines at least \(n\) distinct lines. \textit{X. Chen} and \textit{V. Chávtal} [Discrete Appl. Math. 156, No. 11, 2101--2108 (2008; Zbl 1157.05019)] 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.