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