Tootfinder

Longest paths in trees and isometricity of ultrametric spaces
Oleksiy Dovgoshey, Olga Rovenska
https://arxiv.org/abs/2510.10038 https://arxiv.org/pdf/2510.…

Longest paths in trees and isometricity of ultrametric spaces
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.