Simultaneous Geometric Graph EmbeddingsEstrellaBalderrama, Alejandro and Gassner, Elisabeth and Jünger, Michael and Percan, Merijam and Schaefer, Marcus and Schulz, Michael (2008) Simultaneous Geometric Graph Embeddings. In: Graph Drawing 15th International Symposium, GD 2007, September 2426, 2007 , pp. 280290(Official URL: http://dx.doi.org/10.1007/9783540775379_28). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540775379_28
AbstractWe 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 straightline drawing is planar. We partially settle an open problem of Erten and Kobourov [5] by showing that even for two graphs the problem is NPhard. We also show that the problem of computing the rectilinear crossing number of a graph can be reduced to a simultaneous geometric graph embedding problem; this implies that placing SGE in NP will be hard, since the corresponding question for rectilinear crossing number is a longstanding open problem. However, rather like rectilinear crossing number, SGE can be decided in PSPACE.
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