A de Bruijn-Erdős theorem for 1–2 metric spaces
Vašek Chvátal · Czechoslovak Mathematical Journal · 2014
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 Chvátal 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.