【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S_h上有三角剖分嵌入,那么G在S_k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。更多还原

【Abstract】 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.更多还原