Abstract
In order to prove, the Map Color Theorem we only have to determine the genus and the non-orientable genus of the complete graph K n , according to Theorems 4.9 and 4.10. That means we just have to prove Eqs. (4.13) and (4.19). Denote the right hand side of (4.13) by p and that of (4.19) by q. Then we have to exhibit an embedding of K n into S p and into N q . The following table shows the values of p and q respectively for small values of n.
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© 1974 Springer-Verlag Berlin Heidelberg
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Ringel, G. (1974). Combinatorics of Embeddings. In: Map Color Theorem. Die Grundlehren der mathematischen Wissenschaften, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65759-7_5
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DOI: https://doi.org/10.1007/978-3-642-65759-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65761-0
Online ISBN: 978-3-642-65759-7
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