Recognizing outerplanar graphs in linear time
International Workshop WG '86 on Graph-theoretic concepts in computer science
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
A lower bound on the size of universal sets for planar graphs
ACM SIGACT News
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
A 1.235 lower bound on the number of points needed to draw all n-vertex planar graphs
Information Processing Letters
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Computing upward topological book embeddings of upward planar digraphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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In this paper we consider the problem of characterizing the directed graphs that admit an upward straight-line embedding into every point set in convex or in general position. In particular, we show that no biconnected directed graph admits an upward straight-line embedding into every point set in convex position, and we provide a characterization of the Hamiltonian directed graphs that admit upward straight-line embeddings into every point set in general or in convex position. We also describe how to construct upward straight-line embeddings of directed paths into convex point sets and we prove that for directed trees such embeddings do not always exist. Further, we investigate the related problem of upward simultaneous embedding without mapping, proving that deciding whether two directed graphs admit an upward simultaneous embedding without mapping is $\cal NP$-hard.