Aboulker, PierreLagarde, GuillaumeMalec, DavidMethuku, AbhishekTompkins, Casey2024-06-182024-06-182017-05Discrete Mathematics Volume 340, Issue 5, Pages 995 - 9991 May 20170012-365Xhttps://repositorio.unab.cl/handle/ria/57732Indexación: ScopusA classical theorem of De Bruijn and Erdős asserts that any noncollinear set of n points in the plane determines at least n distinct lines. We prove that an analogue of this theorem holds for posets, where lines are defined using the natural betweenness relation in posets. More precisely, we obtain a bound on the number of lines depending on the height of the poset. The extremal configurations are also determined. Finally, we introduce a new notion of lines in graphs and show that our result for posets can be extended to this setting. © 2017 Elsevier B.V.enBetweennessDe Bruijn–Erdős theoremLinesArtículoATRIBUCIÓN-NOCOMERCIAL-SINDERIVADAS 4.0 INTERNACIONAL CC BY-NC-ND 4.0 Deed10.1016/j.disc.2017.01.012