Triangular imbeddings of regular graphs

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.