Geodesic
Triangular imbeddings of regular graphs
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 459-469

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It is shown that, among regular graphs with $n$ vertices of degree $\rho$, a graph triangulating an orientable surface of genus $\gamma=1+\frac{\rho-6}{12}n$ exists if and only if $(\rho-6)n\equiv0$ $(\operatorname{mod}12)$. A triangular imbedding for all such graphs is obtained with the help of the technique of flow graphs. Figures: 8. Bibliography: 5 titles. 
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     author = {A. G. Vantsyan},
     title = {Triangular imbeddings of regular graphs},
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A. G. Vantsyan. Triangular imbeddings of regular graphs. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 459-469. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a3/