On the number of cut locus structures on graphs

2011/03/09 by Itoh, Jin-ichi, Vîlcu, Costin
#05C10 #53C22 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1103.1764

Abstract

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 realizations.

Related

• Every graph is a cut locus
• Orientable cut locus structures on graphs
• Cut locus structures on graphs
• The Structure Theorem for The cut locus of a Certain Class of Cylinders\n of Revolution II
• Cut and pendant vertices and the number of connected induced subgraphs of a graph