Table of Contents
ISRN Geometry
Volume 2013, Article ID 328095, 6 pages
http://dx.doi.org/10.1155/2013/328095
Research Article

On the Existence of a Point Subset with 3 or 6 Interior Points

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani 12121, Thailand

Received 11 September 2013; Accepted 31 October 2013

Academic Editors: S. Hernández, A. Stipsicz, and S. Troubetzkoy

Copyright © 2013 Banyat Sroysang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For any finite planar point set in general position, an interior point of the set is a point of the set such that it is not on the boundary of the convex hull of the set . For any positive integer , let be the smallest integer such that every finite planar point set with no three collinear points and with at least interior points has a subset for which the interior of the convex hull of the set contains exactly or interior points of the set . In this paper, we prove that .