This article is cited in 4 papers

Papers published in the English version of the journal

On the Minimum Size of a Point Set Containing a 5-Hole and Double Disjoint 3-Holes

X. You, X. L. Wei

College of Science, Hebei University of Science and Technology, Shijiazhuang, China

Abstract: Let $n(k,l,m)$, $k\leq l\leq m$, be the smallest integer such that any finite planar point set of 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, which are all pairwise disjoint. In this paper we prove that $n(3,3,5)=12$.

Keywords: finite planar point set, $k$-hole, general position, pairwise disjoint holes problems.

Received: 14.11.2012
Revised: 02.02.2015

Language: English

 English version: Mathematical Notes, 2015, 97:6, 951–960

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