Results 221 to 230 of about 71,285 (269)
An Algorithm for Straight-Line Drawing of Planar Graphs
Algorithmica, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Harel, Meir Sardas
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Theoretical and practical results on straight skeletons of planar straight-line graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 We study straight skeletons and make both theoretical and practical contributions which support new approaches to the computation of straight skeletons of arbitrary planar straight-line graphs (PSLGs). We start with an adequate extension of the concept of motorcycle graphs to PSLGs, with motorcycles starting at the reflex vertices of a PSLG, which ...
Stefan Huber, Martin Held
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Optimal Parallel Algorithms for Straight-Line Grid Embeddings of Planar Graphs
SIAM Journal on Discrete Mathematics, 1994 This paper presents two optimal linear work algorithms for computing straight-line grid embeddings of planar graphs. Given a combinatorial embedding of the input graph (with \(n\geq 3\) vertices) a straight-line embedding on a grid of size \((n- 2)\times (n- 2)\) can be computed deterministically in \(O(\log n\log\log n)\) time with \(n/\log n\log\log ...
Ming‐Yang Kao +3 more
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Density of straight-line 1-planar graph drawings
Information Processing Letters, 2013 A 1-planar drawing of a graph is such that each edge is crossed at most once. In 1997, Pach and Toth showed that any 1-planar drawing with n vertices has at most 4n-8 edges and that this bound is tight for n>=12. We show that, in fact, 1-planar drawings with n vertices have at most 4n-9 edges, if we require that the edges are straight-line segments. We
Walter Didimo
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Straight-line grid drawings of planar graphs with linear area
2007 6th International Asia-Pacific Symposium on Visualization, 2007 A straight-line grid drawing of a planar graph G 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. It is well known that a planar graph of n vertices admits a straight-line grid drawing on a grid of area O(n2).
Md Rezaul Karim, Md. Saidur Rahman
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Constrained Tri-Connected Planar Straight Line Graphs
, 2012 It is known that for any set V of n ≥ 4 points in the plane, not in convex position, there is a 3-connected planar straight line graph G = (V, E) with at most 2n − 2 edges, and this bound is the best possible. We show that the upper bound | E | ≤ 2n continues to hold if G = (V, E) is constrained to contain a given graph G 0 = (V, E 0), which is either ...
Marwan Al-Jubeh +5 more
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Tri-Edge-Connectivity Augmentation for Planar Straight Line Graphs
International Symposium on Algorithms and Computation, 2009It is shown that if a planar straight line graph (Pslg) with n vertices in general position in the plane can be augmented to a 3-edge-connected Pslg, then 2n ? 2 new edges are enough for the augmentation. This bound is tight: there are Pslgs with n ? 4 vertices such that any augmentation to a 3-edge-connected Pslg requires 2n ? 2 new edges.
Marwan Al-Jubeh +4 more
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An algorithm for straight-line representation of simple planar graphs
Journal of the Franklin Institute, 1969 Abstract An algorithm is developed for drawing straight-line planar graphs which are isomorphic to a convex polyhedron and simple (i.e. a connected graph with no self-loops or multiple branches). The construction of such graphs is outlined in three stages.
L. S. Woo
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On simultaneous straight-line grid embedding of a planar graph and its dual
Information Processing Letters, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Huaming, He, Xin
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