Results 221 to 230 of about 69,266 (252)

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
semanticscholar   +4 more sources

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
semanticscholar   +4 more sources

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
semanticscholar   +5 more sources

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
semanticscholar   +4 more sources

On simultaneous straight-line grid embedding of a planar graph and its dual

Information Processing Letters, 2006
Simultaneous representations of planar graphs and their duals normally require that the dual vertices to be placed inside their corresponding primal faces, and the edges of the dual graph to cross only their corresponding primal edges. Erten and Kobourov [C. Erten, S.G. Kobourov, Simultaneous embedding of a planar graph and its dual on the grid, Theory
Huaming Zhang, Xin He
semanticscholar   +4 more sources

Tri-Edge-Connectivity Augmentation for Planar Straight Line Graphs

International Symposium on Algorithms and Computation, 2009
It 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, Mashhood Ishaque, Kristóf Rédei, Diane L. Souvaine, Csaba D. Tóth   +4 more
semanticscholar   +4 more sources

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, Martin Fürer, Xin He, Balaji Raghavachari   +3 more
semanticscholar   +5 more sources

Straight Line Representations of Infinite Planar Graphs

Journal of the London Mathematical Society, 1977
graphs are denoted by capital roman letters and plane graphs by capital greek letters. If the graph G is isomorphic to the plane graph F, then F is a representation of G.
Carsten Thomassen
semanticscholar   +5 more sources

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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 ...
Csaba D. Tóth, Csaba D. Tóth, Mashhood Ishaque, Diane L. Souvaine, Andrew Winslow, Marwan Al-Jubeh, Gill Barequet, Gill Barequet   +7 more
openaire   +3 more sources

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
openalex   +4 more sources