Labeled Trees Generating Separable and Locally Finite Ultrametrics

: Dovgoshey, Oleksiy; Rovenska, Olga

Publisher: Springer Nature

: 2026

Annals of Combinatorics

: 0218-0006

: 0219-3094

DOI: https://doi.org/10.1007/s00026-026-00806-0

: https://doi.org/10.1007/s00026-026-00806-0

: https://arxiv.org/pdf/2506.03853

: https://arxiv.org/abs/2506.03853v1

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 those that generate locally finite ultrametric spaces. In particular, we establish an analog of König’s Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.

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The first author was supported by Grant 359772 of the Academy of Finland.