Lower bounds for the number of small convex \(k\)-holes

DOI10.1016/j.comgeo.2013.12.002zbMath1287.65011OpenAlexW2169353964WikidataQ61732473 ScholiaQ61732473MaRDI QIDQ2444312

Thomas Hackl, Alexander Pilz, Clemens Huemer, Birgit Vogtenhuber, Ruy Fabila-Monroy, Oswin Aichholzer

Publication date: 9 April 2014

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2013.12.002

zbMATH Keywords

empty convex polygonconvex \(k\)-holecounting boundsErdős-type problem

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (8)

The number of empty four-gons in random point sets ⋮ Almost empty monochromatic triangles in planar point sets ⋮ Empty triangles in generalized twisted drawings of \(K_n\) ⋮ On \(k\)-gons and \(k\)-holes in point sets ⋮ Maximum Rectilinear Convex Subsets ⋮ Empty rainbow triangles in \(k\)-colored point sets ⋮ A superlinear lower bound on the number of 5-holes ⋮ Empty triangles in good drawings of the complete graph

Cites Work

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• Konvexe Fünfecke in ebenen Punktmengen
• On empty convex polygons in a planar point set
• The empty hexagon theorem
• Empty convex hexagons in planar point sets
• Sets with No Empty Convex 7-Gons
• Empty Simplices in Euclidean Space
• On 5-Gons and 5-Holes
• A Note on the Number of Empty Triangles
• Planar point sets with a small number of empty convex polygons

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