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 -