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Upward Planar Drawings with Three and More Slopes

Journal of Graph Algorithms and Applications, 2023
The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing.
Jonathan Klawitter, Johannes Zink
doaj   +1 more source

Drawing planar graphs with many collinear vertices

Journal of Computational Geometry, 2018
Consider the following problem: Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices?
Giordano Da Lozzo, Vida Dujmović, Fabrizio Frati, Tamara Mchedlidze, Vincenzo Roselli   +4 more
doaj   +1 more source

A Note on Minimum-Segment Drawings of Planar Graphs

Journal of Graph Algorithms and Applications, 2013
A straight-line drawing of a planar graph G is a planar drawing of G such that each vertex is mapped to a point on the Euclidean plane, each edge is drawn as a straight line segment, and no two edges intersect except possibly at a common endpoint ...
Stephane Durocher, Debajyoti Mondal, Rahnuma Islam Nishat, Sue Whitesides   +3 more
doaj   +1 more source

Geometric RAC Simultaneous Drawings of Graphs

Journal of Graph Algorithms and Applications, 2013
In this paper, we study the geometric RAC simultaneous drawing problem: Given two planar graphs that share a common vertex set, a geometric RAC simultaneous drawing is a straight-line drawing in which each graph is drawn planar, there are no edge ...
Evmorfia Argyriou, Michael Bekos, Michael Kaufmann, Antonios Symvonis   +3 more
doaj   +1 more source

Characterizing Families of Cuts that can be Represented by Axis-Parallel Rectangles

Journal of Graph Algorithms and Applications, 2005
A drawing of a family of cuts of a graph is an augmented drawing of the graph such that every cut in the family is represented by a simple closed curve and vice versa.
Ulrik Brandes, Sabine Cornelsen, Dorothea Wagner   +2 more
doaj   +1 more source

Orthogonal-Ordering Constraints are Tough

Journal of Graph Algorithms and Applications, 2013
We show that rectilinear graph drawing, the core problem of bend-minimum orthogonal graph drawing, and uniform edge-length drawing, the core problem of force-directed placement, are NP-hard even for embedded paths if subjected to orthogonal ...
Ulrik Brandes, Barbara Pampel
doaj   +1 more source

Minimum-Area Drawings of Plane 3-Trees

Journal of Graph Algorithms and Applications, 2011
A straight-line grid drawing of a plane graph G is a planar drawing of G, where each vertex is drawn at a grid point of an integer grid and each edge is drawn as a straight-line segment.
Debajyoti Mondal, Rahnuma Islam Nishat, Md. Saidur Rahman, Muhammad Jawaherul Alam   +3 more
doaj   +1 more source

Modifying Orthogonal Drawings for Label Placement

Algorithms, 2016
In this paper, we investigate how one can modify an orthogonal graph drawing to accommodate the placement of overlap-free labels with the minimum cost (i.e., minimum increase of the area and preservation of the quality of the drawing).
Konstantinos G. Kakoulis, Ioannis G. Tollis   +1 more
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Thickness and antithickness of graphs

Journal of Computational Geometry, 2018
This paper studies questions about duality between crossings and non-crossings in graph drawings via the notions of thickness and antithickness. The thickness of a graph $G$ is the minimum integer $k$ such that in some drawing of $G$, the edges can be ...
Vida Dujmović, David R. Wood
doaj   +1 more source

Smooth Orthogonal Layouts

Journal of Graph Algorithms and Applications, 2013
We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments
Michael Bekos, Michael Kaufmann, Stephen Kobourov, Antonios Symvonis   +3 more
doaj   +1 more source