6 citations · 29 across the 16 of their papers we have counts for
5 papers · 1 filter
Orientable cut locus structures on graphs
Jin-ichi Itoh, Costin Vîlcu
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 . Here, criteria for the orient…
On the number of cut locus structures on graphs
Jin-ichi Itoh, Costin Vîlcu
We proved in another paper that every connected graph can be realized as the cut locus of some point on some riemannian surface. Here we give upper bounds on the number of such rea…
Cut locus structures on graphs
Jin-ichi Itoh, Costin Vîlcu
Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.
Every graph is a cut locus
Jin-ichi Itoh, Costin Vîlcu
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 stabili…
Conical Existence of Closed Curves on Convex Polyhedra
Joseph O'Rourke, Costin Vilcu
Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighbor…