Minimal quadrangulations of nonorientable surfaces
Minimal quadrangulations of nonorientable surfaces
复制标题
不可定向曲面的最小四边形
DOI：
10.1016/0097-3165(89)90014-9
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
G. Ringel
中科院分区：
文献类型：
--
作者：
N. Hartsfield;G. Ringel
设N是一个紧2-流形。N上的多面体称为四边形，如果多面体的每个面都是一个有四个不同顶点的四边形（正方形）;没有两个顶点由一个以上的边连接，并且任何两个不同正方形的交点要么是空的，要么是一个边和最多三个顶点。如果平方数最小，则称N的四边形是最小的。例如，图1示出了投影平面的最小四边形。我们将用$（N）表示N的最小四边形中的正方形数。我们将构造K_i（n-1（mod 4））和一般八面体图的四角嵌入。这两个嵌入确定多面体是最小的四边形的表面。
Let N be a compact 2-manifold. A polyhedron on N is called a quadrangulation if each face of the polyhedron is a quadrangle (square) with four distinct vertices; no two vertices are joined by more than one edge, and the intersection of any two distinct squares is either empty or at most one edge and at most three vertices. A quadrangulation of N is called minimal if the number of squares is minimal. For instance, Fig. 1 shows a minimal quadrangulation of the projective plane. We shall denote the number of squares in a minimal quadrangulation of N by $(N). We shall construct quadrangular embeddings of K, for n-1 (mod 4) and the general octahedral graph. Both of these embeddings determine polyhedra which are minimal quadrangulations of the surfaces.