Longest paths in trees and isometricity of ultrametric spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866918158669971456 |
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| author | Dovgoshey, Oleksiy Rovenska, Olga |
| author_facet | Dovgoshey, Oleksiy Rovenska, Olga |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Longest paths in trees and isometricity of ultrametric spaces Dovgoshey, Oleksiy Rovenska, Olga General Topology 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. |
| title | Longest paths in trees and isometricity of ultrametric spaces |
| topic | General Topology |
| url | https://arxiv.org/abs/2510.10038 |