A Note on the Value About a Disjoint Convex Partition Problem

Abstract

Let \(P\) be a planar point set with no three points collinear. A \(k\)-hole of \(P\) is a convex \(k\)-gon \(H\) such that the vertices of \(H\) are elements of \(P\) and no element of \(P\) lies inside \(H\). In this article, we prove that for any planar \(9\)-point set \(P\) with no three points collinear and at least \(5\) vertices on the boundary of the convex hull, \(P\) contains a \(5\)-hole and a disjoint \(3\)-hole.