Metric graphs of negative type

2025/01/13 by Campbell, Rutger, Hendrey, Kevin, Lund, Ben +1
#05C12 #51F99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.07098

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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