TRIANGULAR IMBEDDINGS OF REGULAR GRAPHS
A G Vancjan · Mathematics of the USSR-Sbornik · 1983
It is shown that, among regular graphs with n vertices of degree ρ, a graph triangulating an orientable surface of genus γ = 1 + (ρ – 6)n/12 exists if and only if (ρ – 6) n ≡ 0 (mod 12). A triangular imbedding for all such graphs is obtained with the help of the technique of flow graphs. Bibliography: 5 titles.