Every graph is a cut locus
arXiv:1103.1759
Abstract
We prove that every connected graph can be realized as the cut locus of some point on some Riemannian surface which, in some cases, has constant curvature. We study the stability of such realizations, and their generic behavior.
16 pages, 3 figures. Second in a series of four papers. Statements in the last section corrected, presentation improved, a few references added. Terminology improved, proof of Prop. 4.1 detailed, Fig. 3 revised