On the Existence of a Point Subset with 3 or 6 Interior Points. (5th December 2013)

• Record Type: Journal Article
• Authors: Sroysang, Banyat
• Other Names: Hernández S. Academic Editor.; Stipsicz A. Academic Editor.; Troubetzkoy S. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2013(2013)
• Publication Date: 2013-12-05
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.1155/2013/328095
• Languages: English
• ISSNs: 2090-6307

Abstract

Abstract : For any finite planar point set P in general position, an interior point of the set P is a point of the set P such that it is not on the boundary of the convex hull of the set P . For any positive integer k ≥ 3, let h ( k ) be the smallest integer such that every finite planar point set P with no three collinear points and with at least h ( k ) interior points has a subset Q for which the interior of the convex hull of the set Q contains exactly k or k + 3 interior points of the set P . In this paper, we prove that h ( 3 ) = 8 .