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On the existence of a point subset with three or five interior points

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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 ≥ 1, 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.

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Authors and Affiliations

  1. Hebei University of Science and Technology, Hebei, China

    Xianglin Wei

  2. Hebei Polytechnic University, Shijiazhuang, Hebei, China

    Wenhua Lan & Ren Ding

Authors
  1. Xianglin Wei
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  2. Wenhua Lan
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  3. Ren Ding
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Corresponding author

Correspondence to Xianglin Wei.

Additional information

Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 105–115.

The text was submitted by the authors in English.

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Wei, X., Lan, W. & Ding, R. On the existence of a point subset with three or five interior points. Math Notes 88, 103–111 (2010). https://doi.org/10.1134/S0001434610070102

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  • DOI: https://doi.org/10.1134/S0001434610070102

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