Abstract
If a graphG is embedded in a manifoldM such that all faces are cells bounded by simple closed curves we say that this is a closed 2-cell embedding ofG inM. We show how to generate the 2-cell embeddings in the projective plane from two minimal graphs and the 2-cell embeddings in the torus from six minimal graphs by vertex splitting and face splitting.
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Barnette, D.W. Generating closed 2-cell embeddings in the torus and the projective plane. Discrete Comput Geom 2, 233–247 (1987). https://doi.org/10.1007/BF02187881
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DOI: https://doi.org/10.1007/BF02187881