Every graph is a cut locus

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  • Itoh Jin-ichi
    Department of Mathematics, Faculty of Education, Kumamoto University
  • Vîlcu Costin
    Simion Stoilow Institute of Mathematics of the Romanian Academy

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説明

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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