E. Petrov

most citedBall-preserving mappings of finite ultrametric spaces

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math.MG2013★ 1 cited

Ball-preserving mappings of finite ultrametric spaces

E. Petrov

It is shown that the rooted trees $T_{X}$ and $T_{Y}$ representing finite ultrametric spaces $X$ and $Y$ are isomorphic if and only if there exists a ball-preserving bijection $F:X\to…

math.MG2012

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 $(X, d)$ the following inequality $|\Sp(X)|\leqslant |X|-1$ holds with $\Sp(X)=\{d(x,y):x,y \…

math.MG2012

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…