Journal of Graph Algorithms and Applications
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Testing Simultaneous Planarity when the Common Graph is 2-Connected
Vol. 17, no. 3, pp. 147-171, 2013. Regular paper.
Abstract 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.
Submitted: December 2011.
Reviewed: November 2012.
Revised: December 2012.
Accepted: February 2013.
Final: February 2013.
Published: March 2013.
Communicated by Joseph S. B. Mitchell