De Bruijn–Erdős-type theorems for graphs and posets

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dc.contributor.authorAboulker, Pierre
dc.contributor.authorLagarde, Guillaume
dc.contributor.authorMalec, David
dc.contributor.authorMethuku, Abhishek
dc.contributor.authorTompkins, Casey
dc.date.accessioned2024-06-18T18:41:36Z
dc.date.available2024-06-18T18:41:36Z
dc.date.issued2017-05
dc.descriptionIndexación: Scopus
dc.description.abstractA 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.
dc.description.urihttps://www.sciencedirect.com/science/article/pii/S0012365X17300122?via%3Dihub
dc.identifier.citationDiscrete Mathematics Volume 340, Issue 5, Pages 995 - 9991 May 2017
dc.identifier.doi10.1016/j.disc.2017.01.012
dc.identifier.issn0012-365X
dc.identifier.urihttps://repositorio.unab.cl/handle/ria/57732
dc.language.isoen
dc.publisherElsevier B.V.
dc.rights.licenseATRIBUCIÓN-NOCOMERCIAL-SINDERIVADAS 4.0 INTERNACIONAL CC BY-NC-ND 4.0 Deed
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subjectBetweenness
dc.subjectDe Bruijn–Erdős theorem
dc.subjectLines
dc.titleDe Bruijn–Erdős-type theorems for graphs and posets
dc.typeArtículo
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