 
Summary: On the Existence of a Point Subset with
4 or 5 Interior Points
David AVIS \Lambda
School of Computer Science, McGill University,
3480 University, Montreal, Quebec, Canada, H3A 2A7
Kiyoshi HOSONO y
and
Masatsugu URABE z
Department of Mathematics, Tokai University,
3201 Orido, Shimizu, Shizuoka, 4248610 Japan
July 11, 2000
1 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 – 1, let h(k) be
the smallest integer such that every set of points in the plane, no three collinear,
containing at least h(k) interior points has a subset of points containing k or
k +1 interior points. We proved that h(3) = 3 in an earlier paper. In this paper
we prove that h(4) = 7.
2 Introduction
Throughout the paper we consider only planar point sets in which no three
