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4-Holes in point sets

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10.1016/j.comgeo.2013.12.004
 
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hdl:2117/26659

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Aichholzer, Oswin
Fabila Monroy, Ruy
Gonzalez Aguilar, Hernan
Hackl, Thomas
Heredia, Marco A.
Huemer, ClemensMés informacióMés informacióMés informació
Urrutia Galicia, Jorge
Vogtenhuber, Birgit
Document typeArticle
Defense date2014-08-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
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.
CitationAichholzer, O. [et al.]. 4-Holes in point sets. "Computational geometry: theory and applications", 01 Agost 2014, vol. 47, núm. 6, p. 644-650. 
URIhttp://hdl.handle.net/2117/26659
DOI10.1016/j.comgeo.2013.12.004
ISSN0925-7721
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  • DCCG - Grup de recerca en geometria computacional, combinatoria i discreta - Articles de revista [85]
  • Departament de Matemàtiques - Articles de revista [2.895]
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