Simultaneous Geometric Graph Embeddings

@inproceedings{EstrellaBalderrama2007SimultaneousGG,
  title={Simultaneous Geometric Graph Embeddings},
  author={Alejandro Estrella-Balderrama and Elisabeth Gassner and Michael J{\"u}nger and Merijam Percan and Marcus Schaefer and Michael Schulz},
  booktitle={Graph Drawing},
  year={2007}
}
We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be placed in the plane in such a way that for each graph the straight-line drawing is planar. We partially settle an open problem of Erten and Kobourov [5] by showing that even for two graphs the problem is NP-hard. We also show that the problem of computing the rectilinear crossing number of a graph can be reduced to a… CONTINUE READING
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