Results 1 to 10 of about 2,825 (206)
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 +4 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
openalex +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
+7 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
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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
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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
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Encompassing colored planar straight line graphs
Computational Geometry, 2007 AbstractConsider a planar straight line graph (PSLG), G, with k connected components, k⩾2. We show that if no component is a singleton, we can always find a vertex in one component that sees an entire edge in another component. This implies that when the vertices of G are colored, so that adjacent vertices have different colors, then (1) we can augment
Ferrán Hurtado +3 more
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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
openalex +4 more sources
Connectivity augmentation in planar straight line graphs
Electronic Notes in Discrete Mathematics, 2011 AbstractIt is shown that every connected planar straight line graph with n≥3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most ⌊(2n−2)/3⌋ new edges. It is also shown that every planar straight line tree with n≥3 vertices has an embedding preserving augmentation to a 2-edge connected planar ...
Csaba D. Tóth
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A Linear Time Algorithm for Constructing Maximally Symmetric Straight Line Drawings of Triconnected Planar Graphs [PDF]
Discrete & Computational Geometry, 2006 Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we employ two steps.
Seok-Hee Hong +2 more
+8 more sources