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The Straight-Line RAC Drawing Problem is NP-Hard [PDF]
Journal of Graph Algorithms and Applications, 2012 A RAC drawing of a graph is a polyline drawing in which every pair of crossing edges intersects at right angle. In this paper, we focus on straight-line RAC drawings and demonstrate an infinite class of graphs with unique RAC combinatorial embedding.
Evmorfia Argyriou +2 more
doaj +3 more sources
Straight-Line Rectangular Drawings of Clustered Graphs [PDF]
Lecture Notes in Computer Science, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fabrizio Frati +2 more
exaly +6 more sources
An Experimental Study on the Ply Number of Straight-line Drawings
Journal of Graph Algorithms and Applications, 2019 The ply number of a drawing is a new criterion of interest for graph drawing. Informally, the ply number of a straight-line drawing of a graph is defined as the maximum number of overlapping disks, where each disk is associated with a vertex and has a ...
Felice De Luca +4 more
doaj +5 more sources
Straight-line drawings of 1-planar graphs
Computational Geometry: Theory and ApplicationsA 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 Brandenburg
exaly +3 more sources
Area-efficient algorithms for straight-line tree drawings
Computational Geometry: Theory and Applications, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chan-Su Shin +2 more
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Area-efficient planar straight-line drawings of outerplanar graphs
Discrete Applied Mathematics, 2007 An outerplanar graph \(G\) with \(n\) vertices and maximal degree \(d\) admits a planar straight-line grid drawing with area \(\mathbf O(dn^{1.48})\) in \(\mathbf O(n)\) time. In case \(d=\mathbf o(n^{0.52})\), \(G\) can be drawn this way in \(\mathbf o(n^2)\) area.
Adrian Rusu
exaly +3 more sources
Transversal structures on triangulations: A combinatorial study and straight-line drawings
Discrete Mathematics, 2009 42 pages, the second version is shorter, focusing on the bijection (with application to counting) and on the graph drawing algorithm.
exaly +3 more sources
Morphing Planar Graph Drawings Through 3D
Computing in Geometry and Topology, 2023 In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n-vertex planar graph, there exists a piecewise-linear ...
Kevin Buchin +6 more
doaj +1 more source
Extending Drawings of Graphs to Arrangements of Pseudolines
Journal of Computational Geometry, 2021 In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line ...
Alan Arroyo +2 more
doaj +1 more source
On Collinear Sets in Straight-Line Drawings [PDF]
, 2011 Several small amendments; 21 pages, 11 ...
Alexander Ravsky, Oleg Verbitsky 0001
openaire +2 more sources