Exponential families of non-isomorphic triangulations of complete graphs
It is shown that for \(n\equiv 7\) or \(19\pmod{36}\), there are at least \(2^{n^2/54- O(n)}\) non-isomorphic triangular embeddings of \(K_n\) in an orientable surface, all of which are face 2-colourable. When \(n\equiv 19\) or \(55\pmod{108}\) this estimate can be increased to \(2^{2n^2/81- O(n)}\). A similar estimate is established for non-orientable embeddings when \(n\equiv 1\) or \(7\pmod{18}\) (and an improved estimate in the cases when \(n\equiv 1\) or \(19\pmod{54}\)).
scientific article; zbMATH DE number 1464307
scientific article