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Journal articles on the topic 'Planarität'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Schubert, Ulrich, Siegfried Hünig, and Alexander Aumüller. "Zur Frage der Planarität von 9,10-Anthrachinonderivaten." Liebigs Annalen der Chemie 1985, no. 6 (June 12, 1985): 1216–22. http://dx.doi.org/10.1002/jlac.198519850612.

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2

Araneda, Juan F., Benedikt Neue, and Warren E. Piers. "Erzwungene Planarität: eine Strategie für stabile, borhaltige π-konjugierte Materialien." Angewandte Chemie 124, no. 40 (August 29, 2012): 10117–19. http://dx.doi.org/10.1002/ange.201205265.

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3

Gerson, Fabian, Javier Lopez, Adolf Krebs, and Wolfgang Rüger. "Radikal-Kationen von sterisch gehinderten Bicycloalkylidenen, ein experimenteller Beitrag zur Frage der Planarität des Ethylen-Radikalkations." Angewandte Chemie 93, no. 1 (January 20, 2006): 106–7. http://dx.doi.org/10.1002/ange.19810930122.

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4

王, 丹. "G^+--的平面性." Advances in Applied Mathematics 07, no. 03 (2018): 237–42. http://dx.doi.org/10.12677/aam.2018.73029.

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5

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

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6

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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7

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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8

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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9

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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10

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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11

Didimo, Walter, Francesco Giordano, and Giuseppe Liotta. "Overlapping Cluster Planarity." Journal of Graph Algorithms and Applications 12, no. 3 (2008): 267–91. http://dx.doi.org/10.7155/jgaa.00167.

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12

Guedes, André Luiz Pires, and Lilian Markenzon. "Directed hypergraph planarity." Pesquisa Operacional 25, no. 3 (December 2005): 383–90. http://dx.doi.org/10.1590/s0101-74382005000300005.

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Directed hypergraphs are generalizations of digraphs and can be used to model binary relations among subsets of a given set. Planarity of hypergraphs was studied by Johnson and Pollak; in this paper we extend the planarity concept to directed hypergraphs. It is known that the planarity of a digraph relies on the planarity of its underlying graph. However, for directed hypergraphs, this property do not apply and we propose a new approach which generalizes the usual concept. We also show that the complexity of the recognition of a directed hypergraph as planar is linear on the size of the hypergraph.

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13

Angelini, P., and G. Da Lozzo. "SEFE = C-Planarity?" Computer Journal 59, no. 12 (August 3, 2016): 1831–38. http://dx.doi.org/10.1093/comjnl/bxw035.

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14

JIANG, BOJU, and SHICHENG WANG. "ACHIRALITY AND PLANARITY." Communications in Contemporary Mathematics 02, no. 03 (August 2000): 299–305. http://dx.doi.org/10.1142/s0219199700000141.

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An embedding of a space Y into the 3-sphere S3 is said to be strictly achiral if its image is pointwise fixed by an orientation reversing homeomorphism of S3. A space Y is said to be abstractly planar if it can be embedded into the 2-sphere S2. We first extend Kuratowski Theorem into a criterion for abstract planarity of polyhedra, then show that a polyhedron has a strictly achiral polyhedral embedding into S3 if and only if it is abstractly planar. Some related higher dimensional examples are also discussed.

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15

Bertolazzi, Di Battista, and Didimo. "Quasi-Upward Planarity." Algorithmica 32, no. 3 (March 2002): 474–506. http://dx.doi.org/10.1007/s00453-001-0083-x.

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16

Angelini, Patrizio, and Michael A. Bekos. "Hierarchical Partial Planarity." Algorithmica 81, no. 6 (November 29, 2018): 2196–221. http://dx.doi.org/10.1007/s00453-018-0530-6.

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17

Garg, Ashim, and Roberto Tamassia. "Upward planarity testing." Order 12, no. 2 (1995): 109–33. http://dx.doi.org/10.1007/bf01108622.

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18

Schaefer, Marcus. "Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants." Journal of Graph Algorithms and Applications 17, no. 4 (2013): 367–440. http://dx.doi.org/10.7155/jgaa.00298.

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19

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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20

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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21

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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22

Liu, Wei-Wei (Xenia), Berdy Weng, Lu-Ming Lai, and Kuang-Hsiung Chen. "Bumping Co-planarity Collocation for Different UBM Size by Geometry Integration." International Symposium on Microelectronics 2019, no. 1 (October 1, 2019): 000476–79. http://dx.doi.org/10.4071/2380-4505-2019.1.000476.

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Abstract Bumping co-planarity is a Cu pillar bump characteristic, that can impact to the joint quality of subsequent flip chip bonding process. The plated bump height variation correlates with lesser co-planarity values. Co-planarity can be minimized by bumping process, however the bumping process window is not adequate for some design features. For example, dummy bump or structure drawback features. This paper provides a methodology to improve co-planarity by collocating oval and circular bump which integrates the solder volume of different bump shapes. The final solder formation is different due to the geometry variation from the oval shape and circular shape. The final solder height can be calculated by mathematical integral from as-plated solder volume. Hence, better co-planarity can be achieved by the proposed method to collocate different bump shapes. The Cu pillar bump collocation design rules can be optimized to minimize co-planarity during initial design realization to minimize quality risks during fabrication..

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23

Ramachandran, Vijaya, and John Reif. "Planarity testing in parallel." Journal of Computer and System Sciences 49, no. 3 (December 1994): 517–61. http://dx.doi.org/10.1016/s0022-0000(05)80070-4.

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24

Gunaydin, Hakan, and Michael D. Bartberger. "Stacking with No Planarity?" ACS Medicinal Chemistry Letters 7, no. 4 (April 6, 2016): 341–44. http://dx.doi.org/10.1021/acsmedchemlett.6b00099.

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25

Wei-Kuan, Shih, and Hsu Wen-Lian. "A new planarity test." Theoretical Computer Science 223, no. 1-2 (July 1999): 179–91. http://dx.doi.org/10.1016/s0304-3975(98)00120-0.

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26

Da Lozzo, Giordano, and Ignaz Rutter. "Planarity of streamed graphs." Theoretical Computer Science 799 (December 2019): 1–21. http://dx.doi.org/10.1016/j.tcs.2019.09.029.

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27

Larsen, Niels Wessel, Sonja Rosenlund Hansen, and Thorvald Pedersen. "Planarity of 1-chloroborepin." Journal of Molecular Structure 780-781 (January 2006): 317–18. http://dx.doi.org/10.1016/j.molstruc.2005.07.008.

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28

de Fraysseix, Hubert. "Trémaux Trees and Planarity." Electronic Notes in Discrete Mathematics 31 (August 2008): 169–80. http://dx.doi.org/10.1016/j.endm.2008.06.035.

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29

Di Battista, G., and E. Nardelli. "Hierarchies and planarity theory." IEEE Transactions on Systems, Man, and Cybernetics 18, no. 6 (1988): 1035–46. http://dx.doi.org/10.1109/21.23105.

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30

DE FRAYSSEIX, HUBERT, PATRICE OSSONA DE MENDEZ, and PIERRE ROSENSTIEHL. "TRÉMAUX TREES AND PLANARITY." International Journal of Foundations of Computer Science 17, no. 05 (October 2006): 1017–29. http://dx.doi.org/10.1142/s0129054106004248.

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We present a simplified version of the DFS-based Left-Right planarity testing and embedding algorithm implemented in Pigale [1, 2], which has been considered as the fastest implemented one [3]. We give here a full justification of the algorithm, based on a topological properties of Trémaux trees.

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31

Di Battista, Giuseppe, and Roberto Tamassia. "On-Line Planarity Testing." SIAM Journal on Computing 25, no. 5 (October 1996): 956–97. http://dx.doi.org/10.1137/s0097539794280736.

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32

CAIRNS, GRANT, and DANIEL M. ELTON. "THE PLANARITY PROBLEM II." Journal of Knot Theory and Its Ramifications 05, no. 02 (April 1996): 137–44. http://dx.doi.org/10.1142/s0218216596000102.

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C.F. Gauss gave a necessary condition for a word to be the intersection sequence of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. Since then several authors have given algorithmic solutions to this problem. In a previous paper, along the lines of Gauss’s original condition, we gave a necessary and sufficient condition for the planarity of “signed” Gauss words. In this present paper we give a solution to the planarity problem for unsigned Gauss words.

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33

Saif, M. T. A., and N. C. MacDonald. "Planarity of large MEMS." Journal of Microelectromechanical Systems 5, no. 2 (June 1996): 79–97. http://dx.doi.org/10.1109/84.506196.

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34

Sitthiwiratham, T., and C. Promsakon. "Planarity of joined graphs." Journal of Discrete Mathematical Sciences and Cryptography 12, no. 1 (February 2009): 63–69. http://dx.doi.org/10.1080/09720529.2009.10698217.

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35

Di Battista, Giuseppe, Roberto Tamassia, and Luca Vismara. "Incremental Convex Planarity Testing." Information and Computation 169, no. 1 (August 2001): 94–126. http://dx.doi.org/10.1006/inco.2001.3031.

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36

Lengauer, Thomas. "Hierarchical planarity testing algorithms." Journal of the ACM 36, no. 3 (July 1989): 474–509. http://dx.doi.org/10.1145/65950.65952.

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37

de Fraysseix, Hubert, and Patrice Ossona de Mendez. "Trémaux trees and planarity." European Journal of Combinatorics 33, no. 3 (April 2012): 279–93. http://dx.doi.org/10.1016/j.ejc.2011.09.012.

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38

Brimkov, Valentin, David Coeurjolly, and Reinhard Klette. "Digital planarity—A review." Discrete Applied Mathematics 155, no. 4 (February 2007): 468–95. http://dx.doi.org/10.1016/j.dam.2006.08.004.

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39

Angelini, Patrizio, and Giordano Da Lozzo. "Clustered Planarity with Pipes." Algorithmica 81, no. 6 (January 30, 2019): 2484–526. http://dx.doi.org/10.1007/s00453-018-00541-w.

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40

HEALY, PATRICK, and KAROL LYNCH. "TWO FIXED-PARAMETER TRACTABLE ALGORITHMS FOR TESTING UPWARD PLANARITY." International Journal of Foundations of Computer Science 17, no. 05 (October 2006): 1095–114. http://dx.doi.org/10.1142/s0129054106004285.

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In this paper we consider the problem of testing an arbitrary digraph G = (V,E) for upward planarity. In particular we describe two fixed-parameter tractable algorithms for testing the upward planarity of G. The first algorithm that we present can test the upward planarity of G in O(2t · t! · |V|2)-time where t is the number of triconnected components of G. The second algorithm that we present uses a standard technique known as kernelisation and can test the upward planarity of G in O(|V|2 + k4 · (2k)!)-time, where k = |E| - |V|.

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41

Elakkiya, A., and M. Yamuna. "Planar Characterization – Graph Domination Graphs." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 949. http://dx.doi.org/10.14419/ijet.v7i4.10.26634.

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42

Fulek, Radoslav, Michael Pelsmajer, and Marcus Schaefer. "Hanani-Tutte for Radial Planarity." Journal of Graph Algorithms and Applications 21, no. 1 (2017): 135–54. http://dx.doi.org/10.7155/jgaa.00408.

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43

Bannister, Michael J., Sergio Cabello, and David Eppstein. "Parameterized Complexity of 1-Planarity." Journal of Graph Algorithms and Applications 22, no. 1 (2018): 23–49. http://dx.doi.org/10.7155/jgaa.00457.

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44

Breza, Martin. "On non-planarity of cyclotetraphosphazenes." Polyhedron 22, no. 24 (November 2003): 3243–48. http://dx.doi.org/10.1016/s0277-5387(03)00472-8.

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45

Urzhumtsev, A. G. "How to calculate planarity restraints." Acta Crystallographica Section A Foundations of Crystallography 47, no. 6 (November 1, 1991): 723–27. http://dx.doi.org/10.1107/s0108767391006268.

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46

Hefetz, Dan, Michael Krivelevich, Miloš Stojaković, and Tibor Szabó. "Planarity, Colorability, and Minor Games." SIAM Journal on Discrete Mathematics 22, no. 1 (January 2008): 194–212. http://dx.doi.org/10.1137/060654414.

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47

Binucci, Carla, Emilio Di Giacomo, Walter Didimo, Fabrizio Montecchiani, Maurizio Patrignani, Antonios Symvonis, and Ioannis G. Tollis. "Fan-planarity: Properties and complexity." Theoretical Computer Science 589 (July 2015): 76–86. http://dx.doi.org/10.1016/j.tcs.2015.04.020.

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48

Manaster, Alfred B., Jeffrey B. Remmel, and James H. Schmerl. "Planarity and minimal path algorithms." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 131–42. http://dx.doi.org/10.1017/s1446788700026550.

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AbstractIn 1981 two notions of effective presentation of countable connected graphs were formulated by J. C. E. Dekker—namely, edge recognition algorithm graphs and minimal path algorithm graphs. In this paper we show that every planar graph has a minimal path algorithm presentation but that some graphs have no minimal path algorithm presentations. We introduce the notion of a shortest distance algorithm graph, show that it lies strictly between the two notions of Dekker, and show that every graph has a shortest distance algorithm presentation. Finally, in contrast to Dekker's result about minimal path algorithm graphs, we produce a shortest distance algorithm graph which has no spanning tree which is an edge recognition algorithm graph.

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49

Giacomo, Emilio Di, Walter Didimo, Giuseppe Liotta, and Matthew Suderman. "k-Spine, 1-bend planarity." Theoretical Computer Science 359, no. 1-3 (August 2006): 148–75. http://dx.doi.org/10.1016/j.tcs.2006.02.024.

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50

Brock, C. P., P. J. DeLaLuz, M. Golinski, M. A. Lloyd, T. C. Vanaman, and D. S. Watt. "Planarity of nitro-substituted phenothiazines." Acta Crystallographica Section B Structural Science 52, no. 4 (August 1, 1996): 713–19. http://dx.doi.org/10.1107/s0108768196000201.

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The structures of three nitro-substituted phenothiazines [1,3,4-trifluoro-2-nitrophenothiazine, 10-(4-chlorobutyl)-1,3,4-trifluoro-2-nitrophenothiazine and 10-(4-chlorobutyl)-3-nitrophenothiazine] have been determined. The first of these red compounds forms infinite stacks in the solid state, in which donor and acceptor regions of the approximately planar molecules alternate. The molecules of the other two compounds, which have folded, or `butterfly', conformations in the solid state, do not form stacks, presumably because the bulky chlorobutyl substituents cannot be accommodated. The very dark color of solid 3-nitrophenothiazine suggests the presence of extended molecular stacks, but crystals suitable for a structure determination could not be obtained.

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