The Complexity of Bendless Three-Dimensional Orthogonal Graph Drawing

  title={The Complexity of Bendless Three-Dimensional Orthogonal Graph Drawing},
  author={David Eppstein},
  journal={J. Graph Algorithms Appl.},
  • D. Eppstein
  • Published 25 September 2007
  • Mathematics
  • J. Graph Algorithms Appl.
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and such that no three points lie on the same axis-parallel line; we call a graph with such an embedding an xyz graph}. We describe a correspondence between xyz graphs and face-colored embeddings of the graph onto two-dimensional manifolds, and we relate… 
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