A Note on the Upper Bound for Disjoint Convex Partitions

Let $n(k,l,m)$, $k\le l\le m$, be the smallest integer such that any finite planar point set which has at least $n(k,l,m)$ points in general position, contains an empty convex $k$-hole, an empty convex $l$-hole and an empty convex $m$-hole, in which the three holes are pairwise disjoint. In this article, we prove that $n(4,4,5)\le 16$.