Light sources, obstructions and spherical orders
Discrete Mathematics
Discrete Mathematics
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
Complexity Theory: Exploring the Limits of Efficient Algorithms
Complexity Theory: Exploring the Limits of Efficient Algorithms
A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information
IEEE Transactions on Visualization and Computer Graphics
Coordinate Assignment for Cyclic Level Graphs
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Upper Bounds for Monotone Planar Circuit Value and Variants
Computational Complexity
Plane drawings of queue and deque graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Evaluating monotone circuits on cylinders, planes and tori
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The duals of upward planar graphs on cylinders
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On the curve complexity of upward planar drawings
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Upward planar drawings on the standing and the rolling cylinders
Computational Geometry: Theory and Applications
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We consider planar upward drawings of directed graphs on arbitrary surfaces where the upward direction is defined by a vector field. This generalizes earlier approaches using surfaces with a fixed embedding in ℝ3 and introduces new classes of planar upward drawable graphs, where some of them even allow cycles. Our approach leads to a classification of planar upward embeddability. In particular, we show the coincidence of the classes of planar upward drawable graphs on the sphere and on the standing cylinder. These classes coincide with the classes of planar upward drawable graphs with a homogeneous field on a cylinder and with a radial field in the plane. A cyclic field in the plane introduces the new class RUP of upward drawable graphs, which can be embedded on a rolling cylinder. We establish strict inclusions for planar upward drawability on the plane, the sphere, the rolling cylinder, and the torus, even for acyclic graphs. Finally, upward drawability remains NP-hard for the standing cylinder and the torus; for the cylinder this was left as an open problem by Limaye et al.