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On the Erdos-Szekeres n-interior-point problem

Bharadwaj, Subramanya BV and Govindarajan, Sathish and Sharma, Karmveer (2014) On the Erdos-Szekeres n-interior-point problem. In: EUROPEAN JOURNAL OF COMBINATORICS, 35 (SI). pp. 86-94.

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Official URL: http://dx.doi.org/10.1016/j.ejc.2013.06.028

Abstract

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: 6th European Conference on Combinatorics, Graph Theory and Applications (EuroComb), Budapest, HUNGARY, AUG 29-SEP 02, 2011
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 30 Oct 2013 06:26
Last Modified: 30 Oct 2013 06:26
URI: http://eprints.iisc.ac.in/id/eprint/47605

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