Every graph is a cut locus

Details Every graph is a cut locus Every graph is a cut locus

2011-03-09

arxiv.org/abs/1103.1759v2

Mathematics

Differential Geometry

14 pages, 3 figures. Second in a series of four papers. Slightly improved presentation and few typos corrected in version 2

Scientific paper

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 also study the stability of such realizations, and their generic
behavior.

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