3-Regular Colored Graphs and Classification of Surfaces
Discrete and Computational Geometry
Motivated by the theory of crystallizations, we consider an equivalence relation on the class of 3-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 4m and (b) there are exactly two such graphs if the number of vertices is 4 m+ 2 for each m≥ 1. Using this, we present a simple proof of the classification of closed surfaces.
Basak, Biplab, "3-Regular Colored Graphs and Classification of Surfaces" (2017). Journal Articles. 2446.