Abstract
For a planar point set P in general position, an empty convex k-gon or a k-hole of P is a convex k-gon H such that the vertices of H are elements of P and no element of P lies inside H. Let n(k 1,k 2, ⋯ ,k l ) be the smallest integer such that any set of n(k 1, ⋯ ,k l ) points contains a k i -hole for each i, 1 ≤ i ≤ l, where the holes are pairwise disjoint. We evaluate such values. In particular, we show that n(1,2,3,4,5) = 15.
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Hosono, K., Urabe, M. (2008). A Minimal Planar Point Set with Specified Disjoint Empty Convex Subsets. In: Ito, H., Kano, M., Katoh, N., Uno, Y. (eds) Computational Geometry and Graph Theory. KyotoCGGT 2007. Lecture Notes in Computer Science, vol 4535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89550-3_10
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DOI: https://doi.org/10.1007/978-3-540-89550-3_10
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