Combinatorial structures on triangulations. II. Local colorings
Combinatorial structures on triangulations. II. Local colorings
复制标题
三角剖分的组合结构。
DOI：
10.1016/0001-8708(73)90016-9
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发表时间：
1973
影响因子：
1.7
通讯作者：
S. Fisk
中科院分区：
文献类型：
--
作者：
S. Fisk
在球面上有很多种“着色”的方法，它们等价于四种着色[3]。在本节中，我们将研究任意可定向二流形上其中三个（四着色、边着色和Heawood着色）之间的关系。我们引入了局部着色的概念，澄清的关系。(1)一个三角剖分K的四色是一个映射：K+ &13，它是单纯的，并且将三角形映射到三角形上。我们称任何具有这两个性质的2-复形之间的映射为非退化映射。U3是四面体，因此K的顶点映射到四个顶点。如果K的两个顶点相邻，则它们之间的边映射到一条边，因此它们映射到不同的顶点。因此，这个定义与通常的定义相同。
On the sphere there are many ways of “coloring” which are equivalent to four coloring [3]. In this section we will study the relationships between three of these-four coloring, edge coloring, and heawood coloring-on an arbitrary orientable two manifold. We introduce the concept of a local coloring which clarifies the relations.(1) A four coloring of a triangulation K is a mapf: K+ &13 which is simplicial and maps triangles onto triangles. We call any map between 2-complexes with these two properties a nondegenerate map. U3 is the tetrahedron, so the vertices of K are mapped to four vertices. If two vertices of K are adjacent, then the edge between them is mapped to an edge, so they map to different vertices. Thus this definition is the same as the usual one.