English

3-regular colored graphs and classification of surfaces

Combinatorics 2017-08-01 v2

Abstract

Motivated by the theory of crystallizations, we consider an equivalence relation on the class of 33-regular colored graphs and prove that up to this equivalence (a) there exists a unique contracted 3-regular colored graph if the number of vertices is 4m4m and (b) there are exactly two such graphs if the number of vertices is 4m+24m+2 for each m1m\geq 1. Using this, we present a simple proof of the classification of closed surfaces.

Keywords

Cite

@article{arxiv.1602.07400,
  title  = {3-regular colored graphs and classification of surfaces},
  author = {Biplab Basak},
  journal= {arXiv preprint arXiv:1602.07400},
  year   = {2017}
}

Comments

9 pages, 8 figures, Minor update. To appear in Discrete & Computational Geometry

R2 v1 2026-06-22T12:56:33.765Z