 
Summary: On the Existence of a Point Subset with
a Specified Number of 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
February 1, 2000
Abstract
An interior point of a finite 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
g(k) be the smallest integer such that every set of points in the plane, no three
collinear, containing at least g(k) interior points has a subset of points containing
exactly k interior points. We prove that g(1) = 1, g(2) = 4, g(3) – 8, and
g(k) – k + 2; k – 4. We also give some related results.
1 Introduction
Throughout the paper we consider only planar point sets in which no three
