Points and triangles in the plane and halving planes in space

B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, Discrete & Computational Geometry 6 (1991) 435–442.

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Abstract
We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(c log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.
Publishing Year
Date Published
1991-12-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
NSF Grant CCR-87-14565
Volume
6
Issue
1
Page
435 - 442
IST-REx-ID

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Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry. 1991;6(1):435-442. doi:10.1007/BF02574700
Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger, R. (1991). Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry, 6(1), 435–442. https://doi.org/10.1007/BF02574700
Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space.” Discrete & Computational Geometry 6, no. 1 (1991): 435–42. https://doi.org/10.1007/BF02574700.
B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” Discrete & Computational Geometry, vol. 6, no. 1, pp. 435–442, 1991.
Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1991. Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry. 6(1), 435–442.
Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” Discrete & Computational Geometry, vol. 6, no. 1, Springer, 1991, pp. 435–42, doi:10.1007/BF02574700.

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