Conference
Large bichromatic point sets admit empty monochromatic 4-gons
| Τίτλος: | Large bichromatic point sets admit empty monochromatic 4-gons |
|---|---|
| Συγγραφείς: | Aichholzer, Oswin, Hackl, Thomas, Huemer, Clemens, Hurtado Díaz, Fernando Alfredo, Vogtenhuber, Birgit |
| Συνεισφορές: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
| Έτος έκδοσης: | 2009 |
| Συλλογή: | Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge |
| Θεματικοί όροι: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, Geometry --Data processing, Geometria computacional |
| Περιγραφή: | 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). ; Postprint (published version) |
| Τύπος εγγράφου: | conference object |
| Περιγραφή αρχείου: | 4 p.; application/pdf |
| Γλώσσα: | English |
| Relation: | http://2009.eurocg.org/abstracts.pdf; https://hdl.handle.net/2117/6394 |
| Διαθεσιμότητα: | https://hdl.handle.net/2117/6394 |
| Rights: | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ ; Open Access ; Attribution-NonCommercial-NoDerivs 3.0 Spain |
| Αριθμός Καταχώρησης: | edsbas.9A9CEB71 |
| Βάση Δεδομένων: | BASE |
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