English

Metric graphs of negative type

Combinatorics 2025-01-27 v2

Abstract

The negative type inequalities of a metric space are closely tied to embeddability. A result by Gupta, Newman, and Rabinovich implies that if a metric graph GG does not contain a theta submetric as an embedding, then GG has negative type. We show the converse: if a metric graph GG contains a theta, then it does not have negative type.

Keywords

Cite

@article{arxiv.2501.07098,
  title  = {Metric graphs of negative type},
  author = {Rutger Campbell and Kevin Hendrey and Ben Lund and Casey Tompkins},
  journal= {arXiv preprint arXiv:2501.07098},
  year   = {2025}
}

Comments

5 pages, 2 figures

R2 v1 2026-06-28T21:04:18.635Z