4-Holes in point sets
We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and minimizing the number of general 4-holes, and maximizing the number of non-conve...
| Autores: | , , , , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/26659 |
| Acceso en línea: | https://hdl.handle.net/2117/26659 https://dx.doi.org/10.1016/j.comgeo.2013.12.004 |
| Access Level: | acceso abierto |
| Palabra clave: | Computer science--Mathematics Erdos-Szekeres type problems k-Holes Empty k-gons Empty convex polygons Theorem Number Informàtica -- Matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
| Sumario: | We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and minimizing the number of general 4-holes, and maximizing the number of non-convex 4-holes. In particular, we show that for n >= 9, the maximum number of general 4-holes is ((pi)(4)); the minimum number of general 4-holes is at least 5/2 n(2) - circle minus(n); and the maximum number of non-convex 4-holes is at least 1/2 n(3) - circle minus(n(2) logn) and at most 1/2 n(3) - circle minus(n(2)). 2014 (c) Elsevier B.V. All rights reserved. |
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