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On the Erdos-Szekeres n-interior point problem

Bharadwaj, Subramanya BV and Govindarajan, Sathish and Sharma, Karmveer (2011) On the Erdos-Szekeres n-interior point problem. In: The Sixth European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2011, 2001, EuroComb.

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Official URL: http://dx.doi.org/10.1016/j.endm.2011.09.023


The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1, every point set in the plane with sufficient number of interior points contains a convex polygon containing exactly n-interior points. This has been proved only for n-3. In this paper, we prove it for pointsets having atmost logarithmic number of convex layers. We also show that any pointset containing atleast n interior points, there exists a 2-convex polygon that contains exactly n-interior points.

Item Type: Conference Paper
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Convex Polygons; Interior Points; Erdos-Szekeres Problem; j-Convexity
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 19 Mar 2013 05:29
Last Modified: 19 Mar 2013 05:29
URI: http://eprints.iisc.ac.in/id/eprint/46029

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