一个关于近-三角剖分嵌入的内插定理

摘要

一个近三角剖分嵌入是指一个图嵌入在一个曲面上,使得至多可能有一个面不是三角面.在本文中我们证明了如下结果:如果一个图G在某个可定向曲面Sh上有三角剖分嵌入,那么G在Sk上有一个近三角剖分嵌入,这里k=h,h+1,…,[β(G)/2],而β(G)是图G的Betti数.%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 Sh, then G has a near-triangular embedding into Sk for k = h,h+1,..., [β(G)/2], where β(G) is the Betti number of G.