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Every graph is a cut locus

2011/03/09 by Jin‐ichi Itoh, Itoh, Jin-ichi, Costin Vîlcu +1
Biochemistry, Genetics and Molecular Biology · #05C62 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Protein Degradation and Inhibitors

paper · pdf · doi:10.48550/arxiv.1103.1759

openalex publication_date 2011/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every connected graph can be realized as the cut locus of some point on some Riemannian surface S which, in some cases, has constant curvature. We study the stability of such realizations, and their generic behavior.

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