38 citations · 90 across the 18 of their papers we have counts for
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Extremal properties and morphisms of finite ultrametric spaces and their representing trees
O. Dovgoshey, E. Petrov, H. -M. Teichert
We study extremal properties of finite ultrametric spaces and related properties of representing trees . The notion of weak similarity for such spaces is introduced and re…
How rigid the finite ultrametric spaces can be?
O. Dovgoshey, E. Petrov, H. -M. Teichert
A metric space is rigid if the isometry group of is trivial. The finite ultrametric spaces with are not rigid since for every such there is a self-isom…
On spaces extremal for the Gomory-Hu inequality
O. Dovgoshey, E. Petrov, H. -M. Teichert
Let be a finite ultrametric space. In 1961 E.C. Gomory and T.C. Hu proved the inequality where . Using weighted Ham…
Ball-preserving mappings of finite ultrametric spaces
E. Petrov
It is shown that the rooted trees and representing finite ultrametric spaces and are isomorphic if and only if there exists a ball-preserving bijection $F:X\to…
On the Gomori-Hu inequality
E. Petrov, O. Dovgoshey
It was proved by Gomori and Hu in 1961 that for every finite nonempty ultrametric space the following inequality $|\Sp(X)|\leqslant |X|-1$ holds with $\Sp(X)=\{d(x,y):x,y \…
Weak similarities of metric and semimetric spaces
Oleksiy Dovgoshey, Evgeniy Petrov
Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strict…