2017/11/03 by Basudeb Datta, Datta, Basudeb, Subhojoy Gupta +1
Computer Science · Engineering · #51M20 #52C20 #57M50 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.1711.01247
openalex publication_date 2017/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface S is geometric, that is, it is combinatorially equivalent to a geodesic triangulation with respect to a constant curvature metric on S, and we list the possibilities. A key ingredient of the proof is to show that any two d-regular triangulations of the plane for d> 6 are combinatorially equivalent. The proof of this uniqueness result, which is of independent interest, is based on an inductive argument involving some combinatorial topology.