Three-dimensional grid drawings of graphs

  • János Pach
  • Torsten Thiele
  • Géza Tóth
Drawings in the Air
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)


A three-dimensional grid drawing of a graph G is a placement of the vertices at distinct integer points so that the straight-line segments representing the edges of G are pairwise non-crossing. It is shown that for any fixed r ≥ 2, every r-colorable graph of n vertices has a three-dimensional grid drawing that fits into a box of volume O(n2). The order of magnitude of this bound cannot be improved.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • János Pach
    • 1
  • Torsten Thiele
    • 1
  • Géza Tóth
    • 1
  1. 1.Courant InstituteNew York UniversityUSA

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