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

H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986) 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, 43(2), 344–349. 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 43, no. 2 (1986): 344–49. 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, 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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