Estimates for the Steiner subrelation and Steiner-Gromov relations / A. S. Pakhomova. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 1. P. 17-25 [Moscow Univ. Math. Bulletin. Vol. 69, N 1, 2014.].
A lower bound for n-pointed Steiner subratio and Steiner-Gromov ratio was obtained. As a corollary of the main theorem, the value of these ratios was calculated for several metric spaces, for example, for philogenetic ones. It was also proved, that any number from 0,5 to 1 could be a Steiner subratio or a Steiner-Gromov ratio of a certain metric space.
Key words: Steiner subratio, Steiner-Gromov ratio, Steiner problem, minimal filling, shortest trees, minimal spanning trees, philogenetic spaces.