Three-Dimensional Grid Drawings with Sub-quadratic Volume

  • Vida Dujmović
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)


A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line-segments representing the edges are pairwise non-crossing. A \(\mathcal{O}(n^{3/2})\) volume bound is proved for three-dimensional grid drawings of graphs with bounded degree, graphs with bounded genus, and graphs with no bounded complete graph as a minor. The previous best bound for these graph families was \(\mathcal{O}(n^{2})\). These results (partially) solve open problems due to Pach, Thiele, and Tóth [Graph Drawing 1997] and Felsner, Liotta, and Wismath [Graph Drawing 2001].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vida Dujmović
    • 1
  • David R. Wood
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

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