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A First Order Logic Definition of Beyond-Planar Graphs
Journal of Graph Algorithms and Applications, 2018 Beyond-planarity is a collective term for classes of graphs that extend the planar graphs and are defined by drawings with restrictions on crossings. Examples are 1-planar, fan-planar, fan-crossing free, and quasi-planar graphs. We define these and other
Franz Brandenburg
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Crossing Numbers of Beyond-Planar Graphs Revisited
Journal of Graph Algorithms and Applications, 2022 Graph drawing beyond planarity focuses on drawings of high visual quality for non-planar graphs which are characterized by certain forbidden (edge) crossing configurations. A natural criterion for the quality of a drawing is the number of edge crossings.
Nathan van Beusekom +2 more
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Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity [PDF]
Journal of Graph Algorithms and Applications, 2020 Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings.
Patrizio Angelini +3 more
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Graph Planarity by Replacing Cliques with Paths
Algorithms, 2020 This paper introduces and studies the following beyond-planarity problem, which we call h-Clique2Path Planarity. Let G be a simple topological graph whose vertices are partitioned into subsets of size at most h, each inducing a clique.
Patrizio Angelini +7 more
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Lecture Notes in Computer Science, 2016 Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)
Fabrizio Frati +2 more
exaly +4 more sources
Tethered UAV Autonomous Knotting on Environmental Structures for Transport [PDF]
Cyborg and Bionic SystemsCable-driven robotic systems are widely adopted for transport tasks due to their high load-bearing efficiency. However, their deployment in unstructured or unknown environments is hindered by the challenge of rapidly and reliably anchoring the cable ...
Rui Jin +5 more
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Adjacency Labelling for Planar Graphs (and Beyond) [PDF]
Journal of the ACM, 2020 We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an n -vertex planar graph G is assigned a (1 + o(1)) log 2 n -bit label and the labels of two vertices u and v are
Vida Dujmovic +5 more
openaire +7 more sources
Beyond the planar limit in ABJM [PDF]
Journal of High Energy Physics, 2012 v2: minor ...
de Mello Koch, R +3 more
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Remote Sensing, 2021 Mobile mapping is in the process of becoming a routinely applied standard tool to support administration of cities. For ensuring the usability of the mobile mapping data it is necessary to have a practical method to evaluate the quality of different ...
Norbert Pfeifer +4 more
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Crossing Numbers of Beyond-Planar Graphs [PDF]
Theoretical Computer Science, 2019 We study the 1-planar, quasi-planar, and fan-planar crossing number in comparison to the (unrestricted) crossing number of graphs. We prove that there are $n$-vertex 1-planar (quasi-planar, fan-planar) graphs such that any 1-planar (quasi-planar, fan-planar) drawing has $Ω(n)$ crossings, while $O(1)$ crossings suffice in a crossing-minimal drawing ...
Markus Chimani +3 more
openaire +5 more sources