Relevant bibliographies by topics / Planarity

Academic literature on the topic 'Planarity'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Planarity"

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Barth, Lukas, Guido Brückner, Paul Jungeblut, and Marcel Radermacher. "Multilevel Planarity." Journal of Graph Algorithms and Applications 25, no. 1 (2021): 151–70. http://dx.doi.org/10.7155/jgaa.00554.

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Hughes, David W. "Planetary planarity." Nature 337, no. 6203 (January 1989): 113. http://dx.doi.org/10.1038/337113a0.

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Guha, S., W. Graupner, R. Resel, M. Chandrasekhar, H. R. Chandrasekhar, R. Glaser, and G. Leising. "Planarity ofparaHexaphenyl." Physical Review Letters 82, no. 18 (May 3, 1999): 3625–28. http://dx.doi.org/10.1103/physrevlett.82.3625.

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Angelini, Patrizio, Giordano Da Lozzo, Giuseppe Di Battista, Valentino Di Donato, Philipp Kindermann, Günter Rote, and Ignaz Rutter. "Windrose Planarity." ACM Transactions on Algorithms 14, no. 4 (October 13, 2018): 1–24. http://dx.doi.org/10.1145/3239561.

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Di Giacomo, Emilio, William J. Lenhart, Giuseppe Liotta, Timothy W. Randolph, and Alessandra Tappini. "(k,p)-planarity: A relaxation of hybrid planarity." Theoretical Computer Science 896 (December 2021): 19–30. http://dx.doi.org/10.1016/j.tcs.2021.09.044.

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Angelini, Patrizio, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Maurizio Patrignani, and Ignaz Rutter. "Beyond level planarity: Cyclic, torus, and simultaneous level planarity." Theoretical Computer Science 804 (January 2020): 161–70. http://dx.doi.org/10.1016/j.tcs.2019.11.024.

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Angelini, Patrizio, Peter Eades, Seok-Hee Hong, Karsten Klein, Stephen Kobourov, Giuseppe Liotta, Alfredo Navarra, and Alessandra Tappini. "Graph Planarity by Replacing Cliques with Paths." Algorithms 13, no. 8 (August 13, 2020): 194. http://dx.doi.org/10.3390/a13080194.

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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. h-Clique2Path Planarity asks whether it is possible to obtain a planar subgraph of G by removing edges from each clique so that the subgraph induced by each subset is a path. We investigate the complexity of this problem in relation to k-planarity. In particular, we prove that h-Clique2Path Planarity is NP-complete even when h=4 and G is a simple 3-plane graph, while it can be solved in linear time when G is a simple 1-plane graph, for any value of h. Our results contribute to the growing fields of hybrid planarity and of graph drawing beyond planarity.
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Klemz, Boris, and Günter Rote. "Ordered Level Planarity and Its Relationship to Geodesic Planarity, Bi-Monotonicity, and Variations of Level Planarity." ACM Transactions on Algorithms 15, no. 4 (October 12, 2019): 1–25. http://dx.doi.org/10.1145/3359587.

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Yin, Shao Hui, Yong Qiang Wang, Ye Peng Li, and Shen Gong. "Experimental Study on Effects of Translational Movement on Surface Planarity in Magnetorheological Planarization Process." Advanced Materials Research 1136 (January 2016): 293–96. http://dx.doi.org/10.4028/www.scientific.net/amr.1136.293.

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To improve surface planarity, a translational movement is added into the magnetorheoloigcal planarization process. To explore effects of some process parameters, including trajectory type, stroke and reciprocate velocity, on surface planarity, a set of finishing experiments are carried out. The results show that planarity is well improved when the trough reciprocates perpendicularly to the air gap. Surface planarity decreases as stoke increases but is hardly affected by reciprocate velocity. Using the magnetorheoloigcal planarization process with addition of translational movement, an ultra-smooth surface with planarity of micron order in PV is achieved on a K9 optical glass.
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Hu, Yan Zhong, Nan Jiang, and Hua Dong Wang. "Research on the Non-Planarity about the Tensor Product of Graphs." Advanced Materials Research 366 (October 2011): 136–40. http://dx.doi.org/10.4028/www.scientific.net/amr.366.136.

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The main purpose of this paper is to study the non-planarity of a graph after the tensor product operation. Introduced the concept of invariant property of graphs concerning some operations. Proved the non-planarity of the graph K3,3 and graph K5 is preserved after the bipartite double cover operation. The main conclusion is that the non-planarity of a graph is a invariant property belonging to the bipartite double cover operation, and hence proved the non-planarity of a graph is preserved after the tensor product operation, and conversely, the planarity of a graph is not preserved after the tensor product operation.
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Dissertations / Theses on the topic "Planarity"

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Fowler, Joe. "Unlabled Level Planarity." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/195812.

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Consider a graph G with vertex set V in which each of the n vertices is assigned a number from the set {1, ..., k} for some positive integer k. This assignment phi is a labeling if all k numbers are used. If phi does not assign adjacent vertices the same label, then phi partitions V into k levels. In a level drawing, the y-coordinate of each vertex matches its label and the edges are drawn strictly y-monotone. This leads to level drawings in the xy-plane where all vertices with label j lie along the line lj = {(x, j) : x in Reals} and where each edge crosses any of the k horizontal lines lj for j in [1..k] at most once. A graph with such a labeling forms a level graph and is level planar if it has a level drawing without crossings.We first consider the class of level trees that are level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). We describe which trees are ULP and provide linear-time level planar drawing algorithms for any labeling. We characterize ULP trees in terms of two forbidden subdivisions so that any other tree must contain a subtree homeomorphic to one of these. We also provide linear-time recognition algorithms for ULP trees. We then extend this characterization to all ULP graphs with five additional forbidden subdivisions, and provide linear-time recogntion and drawing algorithms for any given labeling.
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Bachmaier, Christian. "Circle planarity of level graphs." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973953985.

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Hayer, Matthias. "Testing planarity in linear time." Thesis, Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/30483.

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Taylor, Martyn G. "Planarity testing by path addition." Thesis, University of Kent, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580367.

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The first linear-time planarity testing algorithm was developed in 1974 by Hopcroft and Tarjan (H&T) [32] using a method to split a biconnected graph up into edge disjoint paths and then sequentially embed them to test for planarity (a path addition method). Shortly afterwards Booth and Leuker [5] developed an alternative vertex addition linear-time planarity test, based on the earlier work of Lempel, Evan and Cederbaum [47], using a new PQ-Tree data structure. Since then there have been many developments in PQ- Tree vertex addition (and related PC-Tree edge addition) methods including authors such as: Chiba et al. [14]; Shih & Hsu [35, 69]; Boyer and Myrvold [10, 11]; and Haeupler and Tarjan [29]. In comparison, path addition has changed very little from the original algorithm. In 1984, Williamson [84] showed how H&T's algorithm can be extended to find Kuratowski sub-graphs in the event of a non-planar graph; and, in 1993, Mehlhorn, Mutzel and Naher [53] produced an implementation (in C) of H&T's algorithm and extended it to create a planar embedding of a graph. This has remained the state-of-the-art in path addition algorithms for over a decade. Recently", de Fraysseix formulated an algorithm [15, 17], based on Tremaux Trees and a characterisation of planarity by W. Wu [87]; this may prove to be a highly optimised version of H&T's algorithm but is difficult to definitively prove as only an outline of its planarity testing phase is provided. These authors represent the majority of the work on path addition methods of planarity testing and embedding; indicating that it receives little attention compared to vertex or edge addition methods This thesis attempts to reinvigorate the field of path addition and demonstrates: • How Trernaux Trees, which allow undirected connected graphs to be represented as a simple partial order relationship are fundamentally related to H&T-‘^planarity testing algorithm and includes some related invariant properties of these trees; • That the restriction on H&T's planarity testing algorithm to test undirected biconnected graphs can be relaxed to undirected connected graphs; • How to generate all possible embeddings of a biconnected component and how to extend this to generate all possible embeddings of separable graphs; and • Empirical Testing of various graph types and sizes to validate these results.
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Estrella, Balderrama Alejandro. "Simultaneous Embedding and Level Planarity." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/195738.

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Graphs are a common model for representing information consisting of a set of objects or entities and a set of connections or relations between them. Graph Drawing is concerned with the automatic visualization of graphs in order to make the information useful. That is, a good drawing should be helpful in the application domain where it is used by capturing the relationships in the underlying data. We consider two important problems in automated graph drawing: simultaneous embedding and level planarity. Simultaneous embedding is the problem of drawing multiple graphs while maintaining the readability of each graph independently and preserving the mental map when going from one graph to another. In this case, each graph has the same vertex set (same entities) but different edge sets (different relationships). Level planarity arises in the layout of graphs that contain hierarchical relationships. When drawing graphs in the plane, this translates to a restricted form of planarity where the vertical order of the entities is pre-determined. We consider the computational complexity of the simultaneous embedding problem. In particular, we show that in its generality the simultaneous embedding problem is NP-hard if the edges are drawn as straight-lines. We present algorithms for drawing graphs on predetermined levels, which allow the simultaneous embedding of restricted types of graphs, such as outerplanar graphs, trees and paths. Finally, our practical contribution is a tool that implements known and novel algorithms related to simultaneous embedding and level planarity and can be used both as a visualization software and as an aid to study theoretical problems.
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Klein, Philip N. (Philip Nathan). "An efficient parallel algorithm for planarity." Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/34303.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING
Bibliography: leaves 56-57.
by Philip Nathan Klein.
M.S.
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Heinz, Adrian. "Planarity testing and drawing in Jedit 4.0." Virtual Press, 2001. http://liblink.bsu.edu/uhtbin/catkey/1204201.

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In this project, an enhanced version of Jedit is presented. Jedit is a Graph Editor developed at Ball State University by a group of students under the direction of Dr. Jay Bagga. The following paper describes the new version, named Jedit 4.0.In this version two new algorithms are implemented. These are: Planarity Testing and Planarity Drawing. The first algorithm tests a graph for planarity and the second one makes a planar embedding of the graph in a grid of size (n-2) x (n-2), where n is the order of the graph. Planar graphs have important applications in the fields of computer engineering, architecture, and many others.Jedit 4.0 also includes new features that were not available in earlier versions. The new features include: graph rotation operation, graph complement, drawing of well-known graphs, and credits window. Several modifications and additions to existing features and algorithms have also been carried out.Jedit 4.0 uses swing java technology what provides a more elegant look. Drop down menus have also been added to provide the user an easier way to use Jedit.
Department of Computer Science
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Zschalig, Christian. "Characterizations of Planar Lattices by Left-relations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1240834941828-67021.

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Recently, Formal Concept Analysis has proven to be an efficient method for the analysis and representation of information. However, the possibility to visualize concept hierarchies is being affected by the difficulty of drawing attractive diagrams automatically. Reducing the number of edge crossings seems to increase the readability of those drawings. This dissertation concerns with a mandatory prerequisite of this constraint, namely the characterization and visual representation of planar lattices. The manifold existing approaches and algorithms are thereby considered under a different point of view. It is well known that exactly the planar lattices (or planar posets) possess an additional order ``from left to right''. Our aim in this work is to define left-relations and left-orders more precisely and to describe several aspects of planar lattices with their help. The three approaches employed structure the work in as many parts: Left-relations on lattices allow a more efficient consideration of conjugate orders since they are uniquely determined by the sorting of the meet-irreducibles. Additionally, the restriction on the meet-irreducibles enables us to achieve an intuitive description of standard contexts of planar lattices similar to the consecutive-one property. With the help of left-relations on diagrams, planar lattices can indeed be drawn without edge crossings in the plane. Thereby, lattice-theoretically found left-orders can be detected in the graphical representation again. Furthermore, we modify the left-right-numbering algorithm in order to obtain attribute-additive and plane drawings of planar lattices. Finally, we will consider left-relations on contexts. They turn out to be fairly similar structures to the Ferrers-graphs. Planar lattices can be characterized by a property of these graphs, namely the bipartiteness. We will constructively prove this result. Subsequently, we can design an efficient algorithm that finds all non-similar plane diagrams of a lattice
Die Formale Begriffsanalyse hat sich in den letzten Jahren als effizientes Werkzeug zur Datenanalyse und -repräsentation bewährt. Die Möglichkeit der visuellen Darstellung von Begriffshierarchien wird allerdings durch die Schwierigkeit, ansprechende Diagramme automatisch generieren zu können, beeinträchtigt. Offenbar sind Diagramme mit möglichst wenig Kantenkreuzungen für den menschlichen Anwender leichter lesbar. Diese Arbeit beschäftigt sich mit mit einer diesem Kriterium zugrunde liegenden Vorleistung, nämlich der Charakterisierung und Darstellung planarer Verbände. Die schon existierenden vielfältigen Ansätze und Methoden werden dabei unter einem neuen Gesichtspunkt betrachtet. Bekannterweise besitzen genau die planaren Verbände (bzw. planare geordnete Mengen) eine zusätzliche Ordnung "von links nach rechts". Unser Ziel in dieser Arbeit ist es, solche Links-Relationen bzw. Links-Ordnungen genauer zu definieren und verschiedene Aspekte planarer Verbände mit ihrer Hilfe zu beschreiben. Die insgesamt drei auftretenden Sichtweisen gliedern die Arbeit in ebensoviele Teile: Links-Relationen auf Verbänden erlauben eine effizientere Behandlung konjugierter Ordnungen, da sie durch die Anordnung der Schnitt-Irreduziblen schon eindeutig festgelegt sind. Außerdem erlaubt die Beschränkung auf die Schnitt-Irreduziblen eine anschauliche Beschreibung von Standardkontexten planarer Verbände ähnlich der consecutive-one property. Mit Hilfe der Links-Relationen auf Diagrammen können planare Verbände tatsächlich eben gezeichnet werden. Dabei lassen sich verbandstheoretisch ermittelte Links-Ordnungen in der graphischen Darstellung wieder finden. Weiterhin geben wir in eine Modifikation des left-right-numbering an, mit der planare Verbände merkmaladditiv und eben gezeichnet werden können. Schließlich werden wir Links-Relationen auf Kontexten betrachten. Diese stellen sich als sehr ähnlich zu Ferrers-Graphen heraus. Planare Verbände lassen sich durch eine Eigenschaft dieser Graphen, nämlich die Bipartitheit, charakterisieren. Wir werden dieses Ergebnis konstruktiv beweisen und darauf aufbauend einen effizienten Algorithmus angeben, mit dem alle nicht-ähnlichen ebenen Diagramme eines Verbandes bestimmt werden können
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Nowlin, Jeffrey L. "Planarity in ROMDD's of multiple-valued symmetric functions." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1996. http://handle.dtic.mil/100.2/ADA309273.

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Thesis (M.S. in Electrical Engineering) Naval Postgraduate School, March 1996.
Thesis advisor(s): Jon T. Butler. "March 1996." Bibliography: p. 51. Also available online. Mode of access: World Wide Web.
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Zeranski, Robert [Verfasser]. "Satisfiability Characterizations of Upward Planarity Problems / Robert Zeranski." München : Verlag Dr. Hut, 2014. http://d-nb.info/105155053X/34.

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Books on the topic "Planarity"

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Cai, Jiazhen. An interative version of Hopcroft and Tarjan's planarity testing algorithm. New York: Courant Institute of Mathematical Sciences, New York University, 1987.

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Cai, Jiazhen. An interative version of Hopcroft and Tarjan's planarity testing algorithm. New York: Courant Institute of Mathematical Sciences, New York University, 1987.

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Palānārīnʹhā: Planarins. Tabrīz: Nashr-i Akhtar, 2001.

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Rink, Jochen C., ed. Planarian Regeneration. New York, NY: Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4939-7802-1.

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Roman, Kenk. Revised list of the North American freshwater Planarians (Platyhelminthes:Tricladida:Paludicola). Washington, D.C: Smithsonian Institution Press, 1989.

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Hendricks, P. Preliminary results of an inventory of Algal Cave, Glacier National Park, Montana, for aquatic cave invertebrates. Helena, Mont: Montana Natural Heritage Program, 2000.

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Planarity in ROMDD's of Multiple-Valued Symmetric Functions. Storming Media, 1996.

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Graphs: Block 3: Graphs 3 - Planarity and Colouring (Mathematics and Computing/technology: a Third Level Course). Open University Worldwide, 1995.

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Rink, Jochen C. Planarian Regeneration: Methods and Protocols. Springer New York, 2019.

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Rink, Jochen C. Planarian Regeneration: Methods and Protocols. Springer New York, 2018.

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Book chapters on the topic "Planarity"

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Aldous, Joan M., and Robin J. Wilson. "Planarity." In Graphs and Applications, 242–76. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0467-4_11.

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Wallis, W. D. "Planarity." In A Beginner’s Guide to Graph Theory, 113–22. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4580-9_8.

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Wallis, W. D. "Planarity." In A Beginner’s Guide to Graph Theory, 105–14. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4757-3134-7_8.

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Balakrishnan, R., and K. Ranganathan. "Planarity." In A Textbook of Graph Theory, 152–84. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8505-7_8.

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Melnikov, O., V. Sarvanov, R. Tyshkevich, V. Yemelichev, and I. Zverovich. "Planarity." In Kluwer Texts in the Mathematical Sciences, 93–110. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-1514-0_7.

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Balakrishnan, R., and K. Ranganathan. "Planarity." In A Textbook of Graph Theory, 175–205. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4529-6_8.

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Foulds, L. R. "Planarity." In Universitext, 53–73. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-0933-1_5.

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Henning, Michael A., and Jan H. van Vuuren. "Planarity." In Graph and Network Theory, 393–447. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-03857-0_13.

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Saoub, Karin R. "Planarity." In Graph Theory, 339–72. Boca Raton: CRC Press, 2021. | Series: Textbooks in mathematics: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781138361416-7.

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Cortese, Pier Francesco, and Maurizio Patrignani. "Clustered Planarity = Flat Clustered Planarity." In Lecture Notes in Computer Science, 23–38. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04414-5_2.

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Conference papers on the topic "Planarity"

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Cortese, Pier Francesco, and Giuseppe Di Battista. "Clustered planarity." In the twenty-first annual symposium. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1064092.1064093.

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Di Battista, G., and R. Tamassia. "Incremental planarity testing." In 30th Annual Symposium on Foundations of Computer Science. IEEE, 1989. http://dx.doi.org/10.1109/sfcs.1989.63515.

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Didimo, W., F. Giordano, and G. Liotta. "Overlapping cluster planarity." In Asia-Pacific Symposium on Visualisation 2007. IEEE, 2007. http://dx.doi.org/10.1109/apvis.2007.329278.

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Brückner, Guido, and Ignaz Rutter. "Partial and Constrained Level Planarity." In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2017. http://dx.doi.org/10.1137/1.9781611974782.130.

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Klein, Philip N., and John H. Reif. "An efficient parallel algorithm for planarity." In 27th Annual Symposium on Foundations of Computer Science (sfcs 1986). IEEE, 1986. http://dx.doi.org/10.1109/sfcs.1986.6.

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Angelini, Patrizio, Giuseppe Di Battista, Fabrizio Frati, Vít Jelínek, Jan Kratochvíl, Maurizio Patrignani, and Ignaz Rutter. "Testing Planarity of Partially Embedded Graphs." In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2010. http://dx.doi.org/10.1137/1.9781611973075.19.

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Galil, Zvi, Giuseppe F. Italiano, and Neil Sarnak. "Fully dynamic planarity testing (extended abstract)." In the twenty-fourth annual ACM symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/129712.129761.

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Weibel, Thomas, Christian Daul, Didier Wolf, and Ronald Rosch. "Planarity-enforcing higher-order graph cut." In 2011 18th IEEE International Conference on Image Processing (ICIP 2011). IEEE, 2011. http://dx.doi.org/10.1109/icip.2011.6116539.

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Vannoni, M., and G. Molesini. "Calibration of horizontally-placed planarity standards." In 2008 Conference on Precision Electromagnetic Measurements (CPEM 2008). IEEE, 2008. http://dx.doi.org/10.1109/cpem.2008.4574718.

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Belhedi, Amira, Adrien Bartoli, Vincent Gay-bellile, Steve Bourgeois, Patrick Sayd, and Kamel Hamrouni. "Depth Correction for Depth Camera From Planarity." In British Machine Vision Conference 2012. British Machine Vision Association, 2012. http://dx.doi.org/10.5244/c.26.43.

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Reports on the topic "Planarity"

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Hrebeniuk, Bohdan V. Modification of the analytical gamma-algorithm for the flat layout of the graph. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2882.

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The planarity of graphs is one of the key sections of graph theory. Although a graph is an abstract mathematical object, most often it is graph visualization that makes it easier to study or develop in a particular area, for example, the infrastructure of a city, a company’s management or a website’s web page. In general, in the form of a graph, it is possible to depict any structures that have connections between the elements. But often such structures grow to such dimensions that it is difficult to determine whether it is possible to represent them on a plane without intersecting the bonds. There are many algorithms that solve this issue. One of these is the gamma method. The article identifies its problems and suggests methods for solving them, and also examines ways to achieve them.
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