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 h(k) be the smallest integer such that every set of points in the plane, no three collinear, containing at least h(k) interior points has a subset of points containing k or k + 1 interior points. We proved that h(3) =3 in an earlier paper. In this paper we prove that h(4) = 7.
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References
Avis, D., Hosono, K., Urabe, M.: On the Existence of a Point Subset with a Specified Number of Interior Points (1998) (manuscript)
Erdös, P., Szekeres, G.: A Combinatorial Problem in Geometry. Compositio Mathematica 2, 463–470 (1935)
Horton, J.: Sets with No Empty 7-gons. Canad. Math. Bull. 26, 482–484 (1983)
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© 2000 Springer-Verlag Berlin Heidelberg
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Avis, D., Hosono, K., Urabe, M. (2000). On the Existente of a Point Subset with 4 or 5 Interior Points. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_5
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DOI: https://doi.org/10.1007/978-3-540-46515-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67181-7
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