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Article

A De Bruijn-Erdős Theorem for Chordal Graphs

Electronic Journal of Combinatorics. 2015. Vol. 22. No. 1. P. 1-6.
Beaudou L., Bondy A., Chen X., Chiniforooshan E., Chudnovsky M., Chvátal V., Fraiman N., Zwols Y.

A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chávtal 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.