An Interpolation Theorem for Near-Triangulations
Han Ren · Journal of Mathematical Research and Exposition · 2006
A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface S_h, then G has a near-triangular embedding into S_k for k = h, h + 1.…, [β(G)/2], where β(G) is the Betti number of G.