Olga Rovenska

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math.GN2026

The Gomory-Hu inequality and trees

Oleksiy Dovgoshey, Olga Rovenska

Let $G = (V, E)$ be a finite connected graph with vertex set $V$ and edge set $E$ , and let $U (G)$ be the set of all ultrametric spaces $(V, d_{l})$ generated by vertex labelings $l\colon…

math.GN2026

Center of distances of ultrametric spaces generated by labeled trees

Oleksiy Dovgoshey, Olga Rovenska

The center of distances of a metric space $(X, d)$ is the set $C (X)$ of all $t \in R^{+}$ for which the equation $d (x, p) = t$ has a solution for each $p \in X$ . We prove that the…

math.GN2025

Longest paths in trees and isometricity of ultrametric spaces

Oleksiy Dovgoshey, Olga Rovenska

Let $T$ be a tree of arbitrary finite or infinite order and let $U (T)$ be the set of all ultrametric spaces generated by vertex labelings of $T$ . Let $US$ denote the class of…

math.GN2025

Forbidden Four Cycle, Star Graphs and Isometric Embeddings

Oleksiy Dovgoshey, Olga Rovenska

We prove the necessary and sufficient conditions under which ultrametric spaces of arbitrary infinite cardinality admit isometric embeddings into ultrametric spaces generated by la…

math.GN2025

Labeled Trees Generating Separable and Locally Finite Ultrametrics

Oleksiy Dovgoshey, Olga Rovenska

We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and…

math.GN2025

Compact ultrametric spaces generated by labeled star graphs

Oleksiy Dovgoshey, Omer Cantor, Olga Rovenska

Let US be the class of all ultrametric spaces generated by labeled star graphs. We prove that compact US-spaces are the completions of totally bounded ultrametric spaces generated…