Abstract
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k≥1, let g(k) be the smallest integer such that every planar point set in general position with at least g(k) interior points has a convex subset of points with exactly k interior points of P. In this article, we prove that g(3)=9.
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This research was supported by National Natural Science Foundation of China (10571042, 10701033), NSF of Hebei (A2005000144, A2007000226, A2007000002) and the SF of Hebei Normal University (L2004202).
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Wei, X., Ding, R. More on an Erdős–Szekeres-Type Problem for Interior Points. Discrete Comput Geom 42, 640–653 (2009). https://doi.org/10.1007/s00454-008-9090-x
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DOI: https://doi.org/10.1007/s00454-008-9090-x