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arXiv · 2501.07098

Metric graphs of negative type

Rutger Campbell·Kevin Hendrey·Ben Lund·Casey Tompkins
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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 $G$ does not contain a theta submetric as an embedding, then $G$ has negative type. We show the converse: if a metric graph $G$ contains a theta, then it does not have negative type.

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Rutger Campbell, Kevin Hendrey, Ben Lund, Casey Tompkins. 2025-01-24. Metric graphs of negative type. https://arxiv.org/abs/2501.07098

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