TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Stöckl, Gerd
ID - 4098
IS - 2
JF - Journal of Combinatorial Theory Series A
TI - The number of extreme pairs of finite point-sets in Euclidean spaces
VL - 43
ER -