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Large bichromatic point sets admit empty monochromatic 4-gons
dc.contributor.author | Aichholzer, Oswin |
dc.contributor.author | Hackl, Thomas |
dc.contributor.author | Huemer, Clemens |
dc.contributor.author | Hurtado Díaz, Fernando Alfredo |
dc.contributor.author | Vogtenhuber, Birgit |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2010-02-16T18:48:06Z |
dc.date.available | 2010-02-16T18:48:06Z |
dc.date.created | 2009 |
dc.date.issued | 2009 |
dc.identifier.citation | Aichholzer, O. [et al.]. Large bichromatic point sets admit empty monochromatic 4-gons. A: European Workshop on Computational Geometry. "25th European Workshop on Computational Geometry". 2009, p. 133-136. |
dc.identifier.uri | http://hdl.handle.net/2117/6394 |
dc.description.abstract | We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many). |
dc.format.extent | 4 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional |
dc.subject.lcsh | Geometry --Data processing |
dc.title | Large bichromatic point sets admit empty monochromatic 4-gons |
dc.type | Conference report |
dc.subject.lemac | Geometria computacional |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.relation.publisherversion | http://2009.eurocg.org/abstracts.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 2358687 |
dc.description.version | Postprint (published version) |
local.citation.author | Aichholzer, O.; Hackl, T.; Huemer, C.; Hurtado, F.; Vogtenhuber, B. |
local.citation.contributor | European Workshop on Computational Geometry |
local.citation.publicationName | 25th European Workshop on Computational Geometry |
local.citation.startingPage | 133 |
local.citation.endingPage | 136 |