五个顶点的完全图的边同伦与delta顶点同伦分类

Edge-Homotopy and Delta Vertex-Homotopy Classification of Spatial Complete Graphs on Five Vertices

研究了五个顶点的完全图K5的边同伦分类,证明了K5的两个空间嵌入是边同伦的,当且仅当它们有相同的α-不变量。并举例说明了对存在着无限多个边同伦而非delta顶点同伦的空间嵌入。

The edge-hcmotopy classification of the complete graph Ks on 5 vertices are studied in this paper. It has been proven that the two spatial emheddings of K5 are edge-homotopic, if and only if they have the same α-invariant. Also,an example is given to show that there are many infinite spatial embeddings of Ks up to delta vertex-homotopy which are mutually edge-homotopic.