Abstract
For a planar n point set P in general position, a convex polygon of P is called empty if no point of P lies in its interior. We show that P can be always partitioned into at most ⌈9n/34 ⌉ empty convex polygons and that ⌈(n + 1)/4 ⌉ empty convex polygons are occasionally necessary.
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References
Hosono, K., Urabe, M.: On the number of disjoint convex quadrilaterals for a planar point set. Comp. Geom. Theory Appl. 20, 97–104 (2001)
Urabe, M.: On a partition into convex polygons. Discr. Appl. Math. 64, 179–191 (1996)
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© 2003 Springer-Verlag Berlin Heidelberg
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Ding, R., Hosono, K., Urabe, M., Xu, C. (2003). Partitioning a Planar Point Set into Empty Convex Polygons. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_13
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DOI: https://doi.org/10.1007/978-3-540-44400-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
Online ISBN: 978-3-540-44400-8
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