Sroysang, Banyat An improved lower bound for an Erdős-Szekeres-type problem with interior points. (English) Zbl 1268.52012 Appl. Math. Sci., Ruse 6, No. 69-72, 3453-3459 (2012). Summary: For each finite planar point set \(P\) with no three collinear points, an interior point of \(P\) is a point in \(P\) such that it is not on the boundary of the convex hull of \(P\). For any integer \(k > 0\), let \(g(k)\) be the smallest integer such that every finite planar point set \(P\) with no three collinear points and with at least \(g(k)\) interior points has a subset \(Q\) whose the interior of the convex hull of \(Q\) contains exactly \(k\) points of \(P\). In this paper, we show that \(g(k) \geq k^2\) for all integer \(k\geq 4\). Cited in 2 Documents MSC: 52C10 Erdős problems and related topics of discrete geometry Keywords:interior point; finite planar set; convex hull; deficient point set PDFBibTeX XMLCite \textit{B. Sroysang}, Appl. Math. Sci., Ruse 6, No. 69--72, 3453--3459 (2012; Zbl 1268.52012) Full Text: Link