Combinatorica

, Volume 10, Issue 1, pp 41–51

How to draw a planar graph on a grid

  • H. De Fraysseix
  • J. Pach
  • R. Pollack
Article
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Abstract

Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide anO(n) space,O(n logn) 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 support such an embedding. On the other hand we show that any setF, which can support a Fáry embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.

AMS subject classification (1980)

05C10 05C35 68E10 

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Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • H. De Fraysseix
    • 1
  • J. Pach
    • 2
    • 3
  • R. Pollack
    • 3
  1. 1.CNRSParisFrance
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesHungary
  3. 3.Courant InstituteNYUNew YorkUSA

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