Results 191 to 200 of about 3,062 (225)

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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Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three

Algorithmica, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marwan Al-Jubeh, Mashhood Ishaque, Kristóf Rédei, Diane L. Souvaine, Csaba D. Tóth, Pável Valtr   +5 more
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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, Aleksandar Shurbevski, Hiroshi Nagamochi, Peter Eades   +3 more
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Straight Line Embeddings of Planar Graphs on Point Sets

, 1996
Netzahualcoyotl Castañeda, Jorge Urrutia   +1 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, Mashhood Ishaque, Kristóf Rédei, Diane L. Souvaine, Csaba D. Tóth   +4 more
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Augmenting Planar Straight Line Graphs to 2-Edge-Connectivity

2015
We show that every planar straight line graph PSLG with n vertices can be augmented to a 2-edge-connected PSLG with the addition of at most $$\lfloor 4n-4/3\rfloor $$ new edges. This bound is the best possible.
Hugo Alves Akitaya, Jonathan Castello, Yauheniya Lahoda, Anika Rounds, Csaba D. Tóth   +4 more
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On simultaneous straight-line grid embedding of a planar graph and its dual

Information Processing Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Huaming, He, Xin
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Suppressed recombination loss in organic photovoltaics adopting a planar–mixed heterojunction architecture

Nature Energy, 2022
Kui Jiang, Francis R Lin, Feng Qi
exaly  

The critical role of composition-dependent intragrain planar defects in the performance of MA1–xFAxPbI3 perovskite solar cells

Nature Energy, 2021
Wei Li, Mathias Uller Rothmann, Ye Zhu
exaly  

Straight Line Representations of Infinite Planar Graphs

Journal of the London Mathematical Society, 1977
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