Small sets supporting fary embeddings of planar graphs

@inproceedings{Fraysseix1988SmallSS,
  title={Small sets supporting fary embeddings of planar graphs},
  author={Hubert de Fraysseix and J{\'a}nos Pach and Richard Pollack},
  booktitle={STOC '88},
  year={1988}
}
Answering a question of Rosenstiehl and Tarjan, we show that every plane graph with <italic>n</italic> vertices has a Fáry embedding (i.e., straight-line embedding) on the 2<italic>n</italic> - 4 by <italic>n</italic> - 2 grid and provide an &Ogr;(<italic>n</italic>) space, &Ogr;(<italic>n</italic> log <italic>n</italic>) time algorithm to effect this embedding. The grid size is asymptotically optimal and it had been previously unknown whether one can always find a polynomial sized grid to… 

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