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(k1,k2,⋯, kl ) be the smallest integer such that any set of n(k 1,⋯,kl ) points contains a ki-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. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Hosono, K., & Urabe, M. (2008). A minimal planar point set with specified disjoint empty convex subsets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4535 LNCS, pp. 90–100). Springer Verlag. https://doi.org/10.1007/978-3-540-89550-3_10
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