A Note on the Value in the Disjoint Convex Partition Problem

Let P be a planar point set with no three points collinear; k points of P form a k-hole of P if these k points are the vertices of a convex polygon whose interior contains no points of P. Inthis article, we prove that any planar point set containing at least 13 points with no three points collinear contains pairwise disjoint 3-, 4-, and 5-holes if there exists a separating line SL₄.