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Straight-line Drawability of a Planar Graph Plus an Edge [PDF]
Workshop on Algorithms and Data Structures, 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.
Peter Eades +4 more
core +8 more sources
A Note on Minimum-Area Straight-Line Drawings of Planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 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
semanticscholar +5 more sources
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
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
semanticscholar +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
semanticscholar +7 more sources
Refining a triangulation of a planar straight-line graph to eliminate large angles [PDF]
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, 2002 We show that any planar straight line graph (PSLG) with v vertices can be triangulated with no angle larger than 7/spl pi//8 by adding O(v/sup 2/log v) Steiner points in O(v/sup 2/log/sup 2/ v) time. We first triangulate the PSLG with an arbitrary constrained triangulation and then refine that triangulation by adding additional vertices and edges.
Scott A. Mitchell
semanticscholar +3 more sources
Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 2013 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend.
Md. Jawaherul Alam +2 more
semanticscholar +3 more sources
From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and Morphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The algorithm of Tutte for constructing convex planar straight-line drawings and the algorithm of Floater and Gotsman for constructing planar straight-line morphs are among the most popular graph drawing algorithms.
Giuseppe Di Battista, Fabrizio Frati
doaj +3 more sources
On the Number of Acute Triangles in a Straight-Line Embedding of a Maximal Planar Graph
Journal of Combinatorial Theory, Series B, 1999 We show that any maximal planar graph with \(m\) triangles except the unbounded face can be transformed into a straight-line embedding in which at least \(\lceil m/3\rceil\) triangles are acute triangles. Moreover, we show that any maximal outer-planar graph can be transformed into a straight-line embedding in which all faces are acute triangles except
Atsushi Kaneko +2 more
semanticscholar +3 more sources
Edge-Disjoint Homotopic Paths in Straight-Line Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 1991 Let G be a planar graph, embedded without crossings in the euclidean plane $\mathbb{R}^2 $, and let $I_1 , \cdots ,I_p $ be some of its faces (including the unbounded face), considered as open sets. Suppose there exist (straight) line segments $L_1 , \cdots ,L_t $ in $\mathbb{R}^2 $ so that $G \cup I_1 \cup \cdots \cup I_p = L_1 \cup \cdots \cup L_t ...
Alexander Schrijver
semanticscholar +3 more sources