English

Graph comparison meets Alexandrov

Metric Geometry 2023-06-13 v2 Combinatorics Differential Geometry

Abstract

Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph comparisons.

Keywords

Cite

@article{arxiv.2212.08016,
  title  = {Graph comparison meets Alexandrov},
  author = {Nina Lebedeva and Anton Petrunin},
  journal= {arXiv preprint arXiv:2212.08016},
  year   = {2023}
}

Comments

English+Russian, 7+7 pages, 11+11 figures

R2 v1 2026-06-28T07:37:18.776Z