Orientable cut locus structures on graphs
  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. 
Jin-ichi Itoh and Costin V\^ilcu
math.DG cs.DM