Orientable cut locus structures on graphs

Abstract

We showed in another paper [arXiv:1103.1759] that every connected graph can be realized as the cut locus of some point on some riemannian surface $S$. Here, criteria for the orientability of $S$ are given, and are applied to classify the distinct, orientable, cut locus structures on graphs with four generating cycles.

24 pages, 14 pages. Fourth in a series of four papers

References in corpus (3)

• On the number of cut locus structures on graphs
• Every graph is a cut locus
• Cut locus structures on graphs

Cited by in corpus (2)

• A connection between cut locus, Thom space and Morse-Bott functions
• Every graph is a cut locus