Results 41 to 50 of about 13,763 (118)

Morphing Planar Graph Drawings with Bent Edges

Journal of Graph Algorithms and Applications, 2011
We give an algorithm to morph between two planar drawings of a graph, preserving planarity, but allowing edges to bend during the course of the morph. The morph is polynomial size and discrete: it uses a polynomial number of elementary steps, where each ...
Anna Lubiw, Mark Petrick
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The Price of Upwardness [PDF]

Discrete Mathematics & Theoretical Computer Science
Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the
Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, Alexander Wolff   +10 more
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Halogen Bonding in (Z)-2-Iodocinnamaldehyde

Molecules, 2013
Based on the bulkiness of the iodine atom, a non-planar conformation was expected for the title compound. Instead, its molecular structure is planar, as experimentally determined using single crystal X-ray diffraction, and confirmed theoretically by DFT ...
Miriam Rossi, Pakorn Bovonsombat, Francesco Caruso, Andrew Jdaydani   +3 more
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OOPS: Optimized One-Planarity Solver via SAT

Journal of Graph Algorithms and Applications
We present OOPS (Optimized One-Planarity Solver), a practical heuristic for recognizing 1-planar graphs and several important subclasses. A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once---a natural ...
Sergey Pupyrev
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On the Cutting Edge: Simplified O(n) Planarity by Edge Addition

Journal of Graph Algorithms and Applications, 2004
We present new O(n)-time methods for planar embedding and Kuratowski subgraph isolation that were inspired by the Booth-Lueker PQ-tree implementation of the Lempel-Even-Cederbaum vertex addition method.
John Boyer, Wendy Myrvold
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Beyond Outerplanarity

Computing in Geometry and Topology
We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with convex drawings: outer $k$-planar graphs, where each edge is crossed by at ...
Steven Chaplick, Myroslav Kryven, Giuseppe Liotta, Andre Löffler, Alexander Wolff   +4 more
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A spherical fuzzy planar graph approach to optimize wire configuration in transformers

Frontiers in Physics
In this modern era, graph theory has become an integral part of science and technology. It has enormous applications in handling various design-based problems.
Hao Guan, Hao Guan, Saira Hameed, Sadaf, Aysha Khan, Jana Shafi   +5 more
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Structural Parameterizations of $k$-Planarity

Journal of Graph Algorithms and Applications
The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times.
Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada   +2 more
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Effect of Gurney Flaps on Non-Planar Wings at Low Reynolds Number

Aerospace
The effect of spanwise wing non-planarity, employed in conjunction with a Gurney flap, is presented. Testing was undertaken in a low-speed wind tunnel using a rectangular wing with an aspect ratio of three. The outer one-third of the wing was non-planar,
Lance W. Traub
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Heuristics for Exact 1-Planarity Testing

Journal of Graph Algorithms and Applications
Since many real-world graphs are nonplanar, the study of graphs that allow few crossings per edge has been an active subfield of graph theory in recent years.
Miriam Münch, Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter   +3 more
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