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 Mat. Zametki, 2018, Volume 104, Issue 1, paper published in the English version journal (Mi mz12161)

Papers published in the English version of the journal

A Note on the Value in the Disjoint Convex Partition Problem

Xinshang Youa, Tong Chenb

a College of Economics and Management, Shandong University of Science and Technology, Qingdao, 266590 China
b College of Management and Economics, Tianjin University, Tianjin, 300072 China

Abstract: Let $P$ be a planar point set with no three points collinear; $k$ points of $P$ form a $k$-hole of $P$ if these $k$ points are the vertices of a convex polygon whose interior contains no points of $P$. In this article, we prove that any planar point set containing at least 13 points with no three points collinear contains pairwise disjoint 3-, 4-, and 5-holes if there exists a separating line $SL_{4}$.

Keywords: convex polygon, general position, planar point set, $k$-hole.

 Funding Agency Grant Number Scientific Research Foundation of Shandong University of Science and Technology 2017RCJJ022 National Social Science Fund of China 17BZZ006 National Natural Science Foundation of China 71602144 This work was supported in part by Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents(grant no. 2017RCJJ022), National Social Science Fund of China (grant no. 17BZZ006), National Natural Science Found of China (grant no. 71602144).

English version:
Mathematical Notes, 2018, 104:1, 135–149

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Citation: Xinshang You, Tong Chen, “A Note on the Value in the Disjoint Convex Partition Problem”, Math. Notes, 104:1 (2018), 135–149

Citation in format AMSBIB
\Bibitem{YouChe18} \by Xinshang~You, Tong~Chen \paper A Note on the Value in the Disjoint Convex Partition Problem \jour Math. Notes \yr 2018 \vol 104 \issue 1 \pages 135--149 \mathnet{http://mi.mathnet.ru/mz12161} \crossref{https://doi.org/10.1134/S0001434618070143} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3868961} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500014} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054401708}