Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414728 | Computational Geometry | 2014 | 9 Pages |
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 Erdős-type question on the least number hk(n)hk(n) of convex k-holes in S , and give improved lower bounds on hk(n)hk(n), for 3⩽k⩽53⩽k⩽5. Specifically, we show that h3(n)⩾n2−32n7+227, h4(n)⩾n22−9n4−o(n), and h5(n)⩾3n4−o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Oswin Aichholzer, Ruy Fabila-Monroy, Thomas Hackl, Clemens Huemer, Alexander Pilz, Birgit Vogtenhuber,