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Mat. Sb., 2013, Volume 204, Number 8, Pages 51–72 (Mi msb7925)  

This article is cited in 3 scientific papers (total in 3 papers)

Subdominant pseudoultrametric on graphs

A. A. Dovgoshey, E. A. Petrov

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk

Abstract: Let $(G,w)$ be a weighted graph. We find necessary and sufficient conditions under which the weight $w\colon E(G)\to \mathbb{R}^+$ can be extended to a pseudoultrametric on $V(G)$, and establish a criterion for the uniqueness of such an extension. We demonstrate that $(G,w)$ is a complete $k$-partite graph, for $k \geq 2$, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with $w$. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric.
Bibliography: 14 titles.

Keywords: weighted graph, infinite graph, ultrametric space, shortest path metric, complete $k$-partite graph.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7925

Full text: PDF file (611 kB)
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English version:
Sbornik: Mathematics, 2013, 204:8, 1131–1151

Bibliographic databases:

UDC: 519.173+515.124
MSC: 05C78, 54E35
Received: 19.08.2011 and 27.02.2013

Citation: A. A. Dovgoshey, E. A. Petrov, “Subdominant pseudoultrametric on graphs”, Mat. Sb., 204:8 (2013), 51–72; Sb. Math., 204:8 (2013), 1131–1151

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7925
  • http://mi.mathnet.ru/eng/msb/v204/i8/p51

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. Dovgoshey, E. Petrov, H.-M. Teichert, “On spaces extremal for the Gomory-Hu inequality”, p-Adic Numbers Ultrametric Anal. Appl., 7:2 (2015), 133–142  crossref  mathscinet  zmath  elib  scopus
    2. O. Dovgoshey, E. Petrov, H.-M. Teichert, “How rigid the finite ultrametric spaces can be?”, J. Fixed Point Theory Appl., 19:2 (2017), 1083–1102  crossref  mathscinet  zmath  isi  scopus
    3. V. Bilet, O. Dovgoshey, M. Kucukaslan, E. Petrov, “Minimal universal metric spaces”, Ann. Acad. Sci. Fenn. Math., 42:2 (2017), 1019–1064  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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