A. A. Tuzhilin

collaborators

2 papers

math.MG2024

When the Gromov-Hausdorff distance between finite-dimensional space and its subset is finite?

I. N. Mikhailov, A. A. Tuzhilin

In this paper we prove that the Gromov--Hausdorff distance between $R^{n}$ and its subset $A$ is finite if and only if $A$ is an $ε$ -net in $R^{n}$ for some…

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…