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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 3, Pages 579–584
DOI: https://doi.org/10.33048/smzh.2023.64.310 (Mi smj7782) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Graph comparison meets Alexandrov

N. D. Lebedevaab, A. M. Petruninc

a Saint Petersburg State University
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
c Department of Mathematics, Pennsylvania State University
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DOI: https://doi.org/10.33048/smzh.2023.64.310
Abstract: Graph comparison is a certain type of condition on the metric space encoded by a finite graph. We show that each nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph comparisons.
Keywords: comparison theorems, Alexandrov's comparison, metric comparison.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00070
National Science Foundation DMS-2005279
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-289
The first author was partially supported by the Russian Foundation for Basic Research (Grant no. 20–01–00070); the second author was partially supported by the National Science Foundation (Grant no. DMS–2005279) and the Ministry of Science and Higher Education of the Russian Federation (Grant no. 075–15–2022–289).
Received: 12.02.2023
Revised: 09.03.2023
Accepted: 06.04.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 3, Pages 624–628
DOI: https://doi.org/10.1134/S0037446623030102
Document Type: Article
UDC: 515.124
MSC: 35R30
Language: Russian
Citation: N. D. Lebedeva, A. M. Petrunin, “Graph comparison meets Alexandrov”, Sibirsk. Mat. Zh., 64:3 (2023), 579–584; Siberian Math. J., 64:3 (2023), 624–628
Citation in format AMSBIB
\Bibitem{LebPet23}
\by N.~D.~Lebedeva, A.~M.~Petrunin
\paper Graph comparison meets Alexandrov
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 3
\pages 579--584
\mathnet{http://mi.mathnet.ru/smj7782}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 3
\pages 624--628
\crossref{https://doi.org/10.1134/S0037446623030102}
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