The Steiner subratio is a fundamental characteristic of a metric space, introduced by A. Ivanov and A. Tuzhilin. This work tries to estimate this subratio for five-point sets on a plane and four-point sets in three-dimensional space.
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Ding-Zhu Du, F. K. Hwang, and E. Y. Yao, “The Steiner ratio conjecture is true for five points,” J. Combin. Theory Ser. A, 38, 230–240 (1985).
A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Mat. Sb., 204, No. 9, 51–72 (2013).
A. O. Ivanov and A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012).
I. Laut and E. Stepanova, to appear.
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N. Strelkova, to appear.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 167–179, 2013.
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Ovsyannikov, Z. The Steiner Subratio of Five Points on a Plane and Four Points in Three-Dimensional Space. J Math Sci 203, 864–872 (2014). https://doi.org/10.1007/s10958-014-2178-3
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