Date of this Version
Periodica Mathematica Hungaria
In this paper we obtain the first non-trivial lower bound on the number of disjoint empty convex pentagons in planar points sets. We show that the number of disjoint empty convex pentagons in any set of n points in the plane, no three on a line, is at least ⌊5n/47⌋. This bound can be further improved to (3n−1)/28 for infinitely many n.
This is a pre-print of an article published in Periodica Mathematica Hungaria. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10998-013-9078-z
convex hull, discrete geometry, empty convex polygons, Erdős-Szekeres theorem, pentagons
Bhattacharya, B. B., & Das, S. (2016). Disjoint Empty Convex Pentagons in Planar Point Sets. Periodica Mathematica Hungaria, 66 (1), 73-86. http://dx.doi.org/10.1007/s10998-013-9078-z
Date Posted: 25 October 2018
This document has been peer reviewed.