Linkless embeddings of graphs in 3-space
Linkless embeddings of graphs in 3-space
复制标题
3 空间中图的无链接嵌入
DOI：
10.1090/s0273-0979-1993-00335-5
复制
发表时间：
1993
影响因子：
1.3
通讯作者：
R. Thomas
中科院分区：
文献类型：
--
作者：
N. Robertson;P. Seymour;R. Thomas
我们在3空间中宣布图形的平坦（无连锁）嵌入显示：（i）只有当每个子图的嵌入3个空间的基本组是免费的（ii）时，嵌入是平坦的（ii）。在a上有所不同k 5或k 3,3的细分（iii）。特别是，四个连接图的任何两个平坦嵌入是环境同位素的，或一个是环境的同位素与另一个镜像的环境同位素
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called flat if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the complement in 3-space of the embedding of every subgraph is free. (ii) If two lat embeddings of the same graph are not ambient isotopic, then they differ on a subdivision of K 5 or K 3,3 . (iii) Any flat embedding of a graph can be transformed to any other flat embedding of the same graph by «3-switches», an analog of 2-switches from the theory of planar embeddings. In particular, any two flat embeddings of a 4-connected graph are either ambient isotopic, or one is ambient isotopic to a mirror image of the other