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arXiv · 1602.07400

3-regular colored graphs and classification of surfaces

Biplab Basak
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Abstract

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 $4m+2$ for each $m\geq 1$. Using this, we present a simple proof of the classification of closed surfaces.

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Biplab Basak. 2017-01-17. 3-regular colored graphs and classification of surfaces. https://doi.org/10.1007/s00454-017-9861-3

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