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• W2007434001 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." @default.
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• W2007434001 date "2014-01-01" @default.
• W2007434001 modified "2023-10-14" @default.
• W2007434001 title "On the Erdős–Szekeresn-interior-point problem" @default.
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• W2007434001 doi "https://doi.org/10.1016/j.ejc.2013.06.028" @default.
• W2007434001 hasPublicationYear "2014" @default.
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