The Topology of Bendless Three-Dimensional Orthogonal Graph Drawing

  • David Eppstein
Conference paper

DOI: 10.1007/978-3-642-00219-9_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)
Cite this paper as:
Eppstein D. (2009) The Topology of Bendless Three-Dimensional Orthogonal Graph Drawing. In: Tollis I.G., Patrignani M. (eds) Graph Drawing. GD 2008. Lecture Notes in Computer Science, vol 5417. Springer, Berlin, Heidelberg


We define an xyz graph to be a spatial embedding of a 3-regular graph such that the edges at each vertex are mutually perpendicular and no three points lie on an axis-parallel line. We describe an equivalence between xyz graphs and 3-face-colored polyhedral maps, under which bipartiteness of the graph is equivalent to orientability of the map. We show that planar graphs are xyz graphs if and only if they are bipartite, cubic, and three-connected. It is NP-complete to recognize xyz graphs, but we show how to do this in time O(n2n/2).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David Eppstein
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaIrvineUSA

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