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 -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 and (b) there are exactly two such graphs if the number of vertices is for each . 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