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Classification of Metric Spaces Whose Steiner–Gromov Ratio is Equal to One

Abstract

Several equivalent conditions for the Steiner–Gromov ratio of a metric space to be equal to one are stated, i.e., conditions for each minimal spanning tree in any finite subset of a given metric space to be both a shortest tree and a minimal filling. A complete classification of such spaces is obtained.

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Correspondence to A. S. Pakhomova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 181–189, 2016.

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Pakhomova, A.S. Classification of Metric Spaces Whose Steiner–Gromov Ratio is Equal to One. J Math Sci 248, 636–641 (2020). https://doi.org/10.1007/s10958-020-04900-3

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