The number of extreme pairs of finite point-sets in Euclidean spaces

Edelsbrunner H, Stöckl G. 1986. The number of extreme pairs of finite point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A. 43(2), 344–349.

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Abstract
To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.
Publishing Year
Date Published
1986-11-01
Journal Title
Journal of Combinatorial Theory Series A
Volume
43
Issue
2
Page
344 - 349
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Edelsbrunner H, Stöckl G. The number of extreme pairs of finite point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A. 1986;43(2):344-349. doi:10.1016/0097-3165(86)90075-0
Edelsbrunner, H., & Stöckl, G. (1986). The number of extreme pairs of finite point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A. Elsevier. https://doi.org/10.1016/0097-3165(86)90075-0
Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series A. Elsevier, 1986. https://doi.org/10.1016/0097-3165(86)90075-0.
H. Edelsbrunner and G. Stöckl, “The number of extreme pairs of finite point-sets in Euclidean spaces,” Journal of Combinatorial Theory Series A, vol. 43, no. 2. Elsevier, pp. 344–349, 1986.
Edelsbrunner H, Stöckl G. 1986. The number of extreme pairs of finite point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A. 43(2), 344–349.
Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series A, vol. 43, no. 2, Elsevier, 1986, pp. 344–49, doi:10.1016/0097-3165(86)90075-0.

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