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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Metric transforms and Euclidean embeddings


Authors: M. Deza and H. Maehara
Journal: Trans. Amer. Math. Soc. 317 (1990), 661-671
MSC: Primary 51K05
DOI: https://doi.org/10.1090/S0002-9947-1990-0974513-6
MathSciNet review: 974513
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Abstract: It is proved that if $ 0 \leqslant c \leqslant 0.72/n$ then for any $ n$-point metric space $ (X,d)$, the metric space $ (X,{d^c})$ is isometrically embeddable into a Euclidean space. For $ 6$-point metric space, $ c = \tfrac{1} {2}{\log _2}\tfrac{3} {2}$ is the largest exponent that guarantees the existence of isometric embeddings into a Euclidean space. Such largest exponent is also determined for all $ n$-point graphs with "truncated distance".


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DOI: https://doi.org/10.1090/S0002-9947-1990-0974513-6
Article copyright: © Copyright 1990 American Mathematical Society