4 papers
Longest paths in trees and isometricity of ultrametric spaces
Oleksiy Dovgoshey, Olga Rovenska
Let be a tree of arbitrary finite or infinite order and let be the set of all ultrametric spaces generated by vertex labelings of . Let denote the class of…
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…
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…
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…