This article is cited in 6 papers

More on Planar Point Subsets with a Specified Number of Interior Points

Wei Xiang Lin, Ding Ren

Hebei Normal University

Abstract: An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer $k\ge1$, let $g(k)$ be the smallest integer such that every set $P$ of points in the plane with no three collinear points and with at least $g(k)$ interior points has a subset containing precisely $k$ interior point of $P$. We prove that $g(k)\ge3k$ for $k\ge3$, which improves the known result that $g(k)\ge3k-1$ for $k\ge3$.

Keywords: interior point of a finite planar set, convex hull, deficient point set.

UDC: 514.8

Received: 14.03.2007

DOI: 10.4213/mzm4720

 English version: Mathematical Notes, 2008, 83:5, 684–687

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