Minimal ordered triangulations of surfaces
Zlatan Magajna, Bojan Mohar, Tomaž Pisanski · Journal of Graph Theory · 1986
Abstract A finite simplicial complex is orderable if its simplices are the chains of a poset. For each closed surface an orderable triangulation is given that is minimal with respect to the number of vertices. The construction of minimal ordered triangulations implies that for each surface S the minimal number of vertices of a bipartite graph, which has a quadrilateral embedding into S, is equal to b(S) = ⌈4 + (16 – 8χ)1/2⌉, where χ is the Euler characteristic of S.