18 citations · 27 across the 3 of their papers we have counts for
3 papers
math.MG2015★ 18 cited
The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic
Alexandr Ivanov, Nadezhda Nikolaeva, Alexey Tuzhilin
It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geod…
math.MG2014
Minimal Spanning Trees on Infinite Sets
A. O. Ivanov, A. A. Tuzhilin
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the correspondi…
math.MG2011★ 9 cited
Steiner Ratio for Manifolds
D. Cieslik, A. O. Ivanov, A. A. Tuzhilin
The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of th…