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Lower bounds for the number of small convex k-holes

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10.1016/j.comgeo.2013.12.002
 
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hdl:2117/26660

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Aichholzer, Oswin
Fabila Monroy, Ruy
Hackl, Thomas
Huemer, ClemensMés informacióMés informacióMés informació
Pilz, Alexander
Vogtenhuber, Birgit
Document typeArticle
Defense date2014-07-01
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
Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds on h(k)(n), for 3 <= k <= 5. Specifically, we show that h(3)(n) >= n(2) - 32n/7 + 22/7, h(4)(n) >= n(2)/2 - 9n/4 - o(n), and h(5)(n) >= 3n/4 - o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987. (C) 2013 Elsevier B.V. All rights reserved.
CitationAichholzer, O. [et al.]. Lower bounds for the number of small convex k-holes. "Computational geometry: theory and applications", 01 Juliol 2014, vol. 47, núm. 5, p. 605-613. 
URIhttp://hdl.handle.net/2117/26660
DOI10.1016/j.comgeo.2013.12.002
ISSN0925-7721
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S0925772113001703
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  • DCCG - Grup de recerca en geometria computacional, combinatoria i discreta - Articles de revista [85]
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