Geodesic
Testing Simultaneous Planarity when the Common Graph is 2-Connected
Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 3, pp. 147-171.

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Two planar graphs G1 and G2 sharing some vertices and edges are simultaneously planar if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the shared graph is 2-connected. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them, and the common subgraph is 2-connected.
DOI : 10.7155/jgaa.00289
Keywords: simultaneous embedding, planar graph, PQ tree, graph drawing, planarity test 
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Bernhard Haeupler; Krishnam Raju Jampani; Anna Lubiw. Testing Simultaneous Planarity when the Common Graph is 2-Connected. Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 3, pp. 147-171. doi : 10.7155/jgaa.00289. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00289/

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