Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

Dovgoshey, Oleksiy; Küçükaslan, Mehmet

doi:10.1007/s00026-022-00581-8

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Proposition 41 ([11]1

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2022

2024

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Cited by 8 publications

(1 citation statement)

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“…It is possible to show that in the case when condition (4.2) does not hold, the space X is pseudoultrametric (see [30] for details).…”

Section: Proposition 41 ([11]mentioning

confidence: 99%

Hereditary properties of finite ultrametric spaces

Петров

2022

J Math Sci

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A characterization of finite homogeneous ultrametric spaces and finite ultrametric spaces generated by unrooted labeled trees has been made in terms of representing trees. Finite ultrametric spaces having perfect strictly n-ary trees have been characterized in terms of special graphs connected with the space. A detailed survey of some special classes of finite ultrametric spaces, which were considered in the last ten years, has been given and their hereditary properties have been studied. More precisely, we are interested in the following question. Let X be an arbitrary finite ultrametric space from some given class. Does every subspace of X also belong to this class?

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“…It is possible to show that in the case when condition (4.2) does not hold, the space X is pseudoultrametric (see [30] for details).…”

Section: Proposition 41 ([11]mentioning

confidence: 99%

Hereditary properties of finite ultrametric spaces

Петров

2022

J Math Sci

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show abstract

Bipartite graphs and best proximity pairs

2022

Self Cite

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We say that a bipartite graph G(A, B) with the fixed parts A and B is proximinal if there is a semimetric space (X, d) such that A and B are disjoint proximinal subsets of X and all edges {a, b} satisfy the equality d(a, b) = dist(A, B). It is proved that a bipartite graph G is not isomorphic to any proximinal graph if and only if G is finite and empty. It is also shown that the subgraph induced by all non-isolated vertices of a nonempty bipartite graph G is a disjoint union of complete bipartite graphs if and only if G is isomorphic to a nonempty proximinal graph for an ultrametric space.

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Locally finite ultrametric spaces and labeled trees

Dovgoshey,

Kostikov

2023

J Math Sci

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Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

Cited by 8 publications

References 31 publications

Hereditary properties of finite ultrametric spaces

Hereditary properties of finite ultrametric spaces

Bipartite graphs and best proximity pairs

Locally finite ultrametric spaces and labeled trees

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