Level Planarity Testing in Linear Time
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Characterization of unlabeled level planar trees
GD'06 Proceedings of the 14th international conference on Graph drawing
Two trees which are self–intersecting when drawn simultaneously
GD'05 Proceedings of the 13th international conference on Graph Drawing
Colored simultaneous geometric embeddings
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Simultaneous graph embedding with bends and circular arcs
Computational Geometry: Theory and Applications
Matched Drawability of Graph Pairs and of Graph Triples
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Characterization of unlabeled level planar trees
Computational Geometry: Theory and Applications
Matched drawability of graph pairs and of graph triples
Computational Geometry: Theory and Applications
On a tree and a path with no geometric simultaneous embedding
GD'10 Proceedings of the 18th international conference on Graph drawing
On graphs supported by line sets
GD'10 Proceedings of the 18th international conference on Graph drawing
Computational Geometry: Theory and Applications
Characterization of unlabeled radial level planar graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
Vertex angle and crossing angle resolution of leveled tree drawings
Information Processing Letters
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We present the set of planar graphs that always have a simultaneous geometric embedding with a strictly monotone path on the same set of n vertices, for any of the n! possible mappings. These graphs are equivalent to the set of unlabeled level planar (ULP) graphs that are level planar over all possible labelings. Our contributions are twofold. First, we provide linear time drawing algorithms for ULP graphs. Second, we provide a complete characterization of ULP graphs by showing that any other graph must contain a subgraph homeomorphic to one of seven forbidden graphs.