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Matematicheskie Zametki, 2010, Volume 88, Issue 1, Pages 105–115
DOI: https://doi.org/10.4213/mzm8798 (Mi mzm8798) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Existence of a Point Subset with Three or Five Interior Points

Xianglin Weia, Wenhua Lanb, Ren Dingb

a Hebei University of Science and Technology
b Hebei Polytechnic University
Full-text PDF (583 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8798
Abstract: An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer $k\ge1$, let $h(k)$ be the smallest integer such that every point set in the plane, no three collinear, with at least $h(k)$ interior points, has a subset with $k$ or $k+2$ interior points of $P$. We prove that $h(3)=8$.
Keywords: finite planar point set, interior point.
Received: 30.06.2010
Revised: 30.12.2007
English version:
Mathematical Notes, 2010, Volume 88, Issue 1, Pages 103–111
DOI: https://doi.org/10.1134/S0001434610070102
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Xianglin Wei, Wenhua Lan, Ren Ding, “On the Existence of a Point Subset with Three or Five Interior Points”, Mat. Zametki, 88:1 (2010), 105–115; Math. Notes, 88:1 (2010), 103–111
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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