Results 1 to 10 of about 3,062 (225)
GA for straight-line grid drawings of maximal planar graphs
Egyptian Informatics Journal, 2012 A straight-line grid drawing of a planar graph G of n vertices is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings.
Mohamed A. El-Sayed
doaj +3 more sources
Straight-line Drawability of a Planar Graph Plus an Edge [PDF]
, 2015 We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line ...
Peter Eades +4 more
+6 more sources
Simultaneous straight-line drawing of a planar graph and its rectangular dual [PDF]
, 2015 A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their corresponding primal edges.
Tamara Mchedlidze
+5 more sources
A Note on Minimum-Area Straight-Line Drawings of Planar Graphs [PDF]
, 2008 Despite a long research effort, finding the minimum area for straight-line grid drawings of planar graphs is still an elusive goal. A long-standing lower bound on the area requirement for straight-line drawings of plane graphs was established in 1984 by Dolev, Leighton, and Trickey, who exhibited a family of graphs, known as nested triangles graphs ...
Fabrizio Frati, Maurizio Patrignani
openalex +4 more sources
A Linear Time Algorithm for Constructing Maximally Symmetric Straight Line Drawings of Triconnected Planar Graphs [PDF]
Discrete & Computational Geometry, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seok-Hee Hong +2 more
+7 more sources
Straight-line drawings of 1-planar graphs
Computational Geometry, 2023 A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges, so that edges of the same color do not cross.
Franz J. Brandenburg
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Straight-line realization of planar graphs.
, 2011 Few theorems are known about planar graphs. For, example, Kuratowski proved that a graph is planar if and only if it has no subgraph homeomorphic to K₅ or K₃,₃. It has remained as a direct criterion for determining whether a graph is planar or not. Powerful as the theorem is, it is not always easy to apply.
Luang-hung Shiau
openalex +2 more sources
Study of Neural Network Algorithm for Straight-Line Drawings of Planar Graphs [PDF]
, 2014 Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as the aesthetics and readability of graph drawings depend on the number of edge crossings.
Mohamed A. El-Sayed +2 more
openalex +3 more sources
An exact algorithm for disaster-resilience augmentation of planar straight-line graphs [PDF]
Journal of Global OptimizationAbstract We consider the problem of adding a minimum length set of edges to a geometric graph so that the resultant graph is resilient against partition from the effect of a single disaster. Disasters are modeled by discs of given maximum radius, and a disaster destroys all edges intersecting its interior.
Alexander Westcott, Charl Ras
openalex +3 more sources
Minimum Weight Connectivity Augmentation for Planar Straight-Line Graphs [PDF]
Theoretical Computer Science, 2017 15 pages, 7 figures, to appear in the Proceedings of WALCOM ...
Hugo A. Akitaya +5 more
openalex +4 more sources