Geodesic
The Steiner subratio of five points on a plane and four points in three-dimensional space
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 167-179
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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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Z. N. Ovsyannikov. The Steiner subratio of five points on a plane and four points in three-dimensional space. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 167-179. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a13/

[1] Erëmin A. Yu., “Formula vesa minimalnogo zapolneniya konechnogo metricheskogo prostranstva”, Mat. sb., 204:9 (2013), 51–72 | DOI | Zbl

[2] Ivanov A. O., Tuzhilin A. A., “Odnomernaya problema Gromova o minimalnom zapolnenii”, Mat. sb., 203:5 (2012), 65–118 | DOI | MR | Zbl

[3] Laut I., Stepanova E., V pechati

[4] Rublëva O., arXiv (to appear)

[5] Strelkova N., V pechati

[6] Ding-Zhu Du, Hwang F. K., Yao E. Y., “The Steiner ratio conjecture is true for five points”, J. Combin. Theory Ser. A, 38 (1985), 230–240 | DOI | MR