Every graph is a cut locus

Jin-ichi Itoh; Costin Vîlcu

doi:10.2969/jmsj/06731227

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Every graph is a cut locus

Jin-ichi Itoh, Costin Vîlcu

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Keywords: cut locus, graph

JOURNAL FREE ACCESS

2015 Volume 67 Issue 3 Pages 1227-1238

DOI https://doi.org/10.2969/jmsj/06731227

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Abstract

We show 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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