Every graph is a cut locus
Differential Geometry
2016-08-14 v4
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.
Cite
@article{arxiv.1103.1759,
title = {Every graph is a cut locus},
author = {Jin-ichi Itoh and Costin Vîlcu},
journal= {arXiv preprint arXiv:1103.1759},
year = {2016}
}
Comments
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