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Optimal Parallel Algorithms for Straight-Line Grid Embeddings of Planar Graphs
SIAM Journal on Discrete Mathematics, 1994 A straight-line grid embedding of a planar graph is a drawing of the graph on a plane where the vertices are located at grid points and the edges are represented by nonintersecting segments of straight, lines joining their incident vertices. Given an n-vertex embedded planar graph with $n \geq 3$, a straight-line embedding on a grid of size $( n - 2 ) \
Ming‐Yang Kao +3 more
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Tri-Edge-Connectivity Augmentation for Planar Straight Line Graphs
, 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 +4 more
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Straight Line Representations of Infinite Planar Graphs
Journal of the London Mathematical Society, 1977 Carsten Thomassen
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Acute Constraints in Straight-Line Drawings of Planar Graphs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2019 Seto Akane +3 more
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Straight Line Embeddings of Planar Graphs on Point Sets
, 1996 Netzahualcoyotl Castañeda +1 more
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Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three
Algorithmica, 2011We characterize the planar straight line graphs (Pslgs) that can be augmented to 3-connected and 3-edge-connected Pslgs, respectively. We show that if a Pslg with n vertices can be augmented to a 3-edge-connected Pslg, then at most 2n−2 new edges are always sufficient and sometimes necessary for the augmentation.
Mashhood Ishaque +5 more
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Constrained Tri-Connected Planar Straight Line Graphs
2012It 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 +7 more
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Area-Thickness Trade-Offs for Straight-Line Drawings of Planar Graphs
The Computer Journal, 2016DI GIACOMO, Emilio +3 more
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