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On Some Applications of Graph Theory to Geometry

Published online by Cambridge University Press:  20 November 2018

P. Erdös
P. Erdös*
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary
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Let [Pn(k)] be the class of all subsets Pn(k) 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).Put

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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 968 - 971
Copyright
Copyright © Canadian Mathematical Society 1967

References

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5. Simonovits, M., A method for solving extremal problems in graph theory, Stability problems, to appear in Proceedings of Colloquium on Graph Theory held in Ochary (1966). See also P. Erdös, Extremal problems in graph theory, Proceedings of Symposium on Theory of Graphs and Its Applications held in Smolenice (1963), 29-36.Google Scholar
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