On Some Applications of Graph Theory to Geometry
نویسنده
چکیده
Let [P,(")] be the class of all subsets P, ( ') of the k-dimensional Euclidean space consisting of n distinct points and having diameter 1 . Denote by dk (n, r) the maximum number of times a given distance r can occur among points of a set Pn ( k) . l'ut Dk (n) = max, d, (n, r) . In other words Dk (n) denotes the maximum number of times the same distance can occur between n suitably chosen points in k-dimensional space . Lenz showed that D4 (n) > ±n 2 + en, and by using the method of Lenz and a graph-theoretic result of Stone and myself (1)1 proved (2) that
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تاریخ انتشار 1967