Linkless embeddings of graphs in 3-space

  title={Linkless embeddings of graphs in 3-space},
  author={Neil Robertson and Paul D. Seymour and Robin Thomas},
  journal={Bulletin of the American Mathematical Society},
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… 

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