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Matematicheskie Zametki, 2015, Volume 97, Issue 6, paper published in the English version journal
(Mi mzm10927)
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This article is cited in 3 scientific papers (total in 3 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
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