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arXiv · 2510.10038

Longest paths in trees and isometricity of ultrametric spaces

Oleksiy Dovgoshey·Olga Rovenska
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Abstract

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 ${\bf US}$ denote the class of all ultrametric spaces generated by vertex labelings of star graphs. We prove that the inclusion $U(T)\subseteq {\bf US}$ holds if and only if the longest path in $T$ has a length not exceeding three.

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Oleksiy Dovgoshey, Olga Rovenska. 2025-10-11. Longest paths in trees and isometricity of ultrametric spaces. https://arxiv.org/abs/2510.10038

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