TY - GEN

T1 - Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges

AU - Fowler, J. Joseph

AU - Jünger, Michael

AU - Kobourov, Stephen

AU - Schulz, Michael

PY - 2008

Y1 - 2008

N2 - A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3. This allows us to characterize the class of planar graphs that always have a SEFE with any other planar graph. We also characterize the class of biconnected outerplanar graphs that always have a SEFE with any other outerplanar graph. In both cases, we provide efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

AB - A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3. This allows us to characterize the class of planar graphs that always have a SEFE with any other planar graph. We also characterize the class of biconnected outerplanar graphs that always have a SEFE with any other outerplanar graph. In both cases, we provide efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

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U2 - 10.1007/978-3-540-92248-3_14

DO - 10.1007/978-3-540-92248-3_14

M3 - Conference contribution

AN - SCOPUS:58349101647

SN - 3540922474

SN - 9783540922476

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 158

BT - Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers

T2 - 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008

Y2 - 30 June 2008 through 2 July 2008

ER -