This article is cited in 2 papers

A Note on the Upper Bound for Disjoint Convex Partitions

Xinshang You, Xiang Lin Wei

Hebei University of Science and Technology

Abstract: 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 $n(4,4,5)\le 16$.

Keywords: finite planar point set, convex partition, convex hull, general position, disjoint hole.

UDC: 514.174.5

Received: 20.03.2013

DOI: 10.4213/mzm10483

 English version: Mathematical Notes, 2014, 96:2, 268–274

Bibliographic databases:

• 
• 
• 
• 
•