一个关于球面和环面上嵌入图的近-三角剖分嵌入的内插定理(I)

一个近-三角剖分嵌入是指一个曲面上的嵌入图使得几乎所有的面都是三角形,至多只有一个可能的例外.文中作者证明了如下结论:如果一个图G 在球面S₀(或环面S₁)上有近-三角剖分嵌入,那么G在每一个可定向曲面S_k有近-三角剖分嵌入,其中k=h,h+1,\cdots ,\lfloor\frac{\beta(G)}{2}\rfloor$, 而h=0(或1)并且β(G)是图G的Betti数.特别地,G是上可嵌入的.

Near-trangular Embeddings for Triangulations of the Sphere and the Torus (I)

A near-triangular embedding is a graph embedded into some surface whose facial walks but one are 3-gons. In this paper the authors show that if a graph G is a triangulation of the sphere S₀ (or the torus S₁), then Ghas a near-triangular embedding into S_k for k = h,h+1,\cdots ,\lfloor\frac{\beta(G)}{2}\rfloor$, where h = 0(or 1) and $\beta(G)$ is the Betti number of G.