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Graph Comparison Meets Alexandrov

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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.

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Acknowledgments

We thank Alexander Lytchak for help.

Funding

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).

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    N. D. Lebedeva

  2. St. Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

    N. D. Lebedeva

  3. Mathematical Department, Pennsylvania State University, University Park, USA

    A. M. Petrunin

Authors
  1. N. D. Lebedeva
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  2. A. M. Petrunin
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Corresponding author

Correspondence to N. D. Lebedeva.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 579–584. https://doi.org/10.33048/smzh.2023.64.310

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Lebedeva, N.D., Petrunin, A.M. Graph Comparison Meets Alexandrov. Sib Math J 64, 624–628 (2023). https://doi.org/10.1134/S0037446623030102

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  • DOI: https://doi.org/10.1134/S0037446623030102

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