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Journal articles on the topic 'Planarity'

To see the other types of publications on this topic, follow the link: Planarity.

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

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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2

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

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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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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

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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20

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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21

Blinova, E. V., T. A. Sahnova, I. N. Merkulova, E. A. I. Aidu, V. G. Trunov, R. M. Shahnovich, T. S. Sukhinina, N. S. Zhukova, N. A. Barysheva, and I. I. Staroverov. "New possibilities of electrocardiography: evaluation of the vectorcardiographic QRS loop planarity in patients with myocardial infarction." Eurasian heart journal, no. 4 (December 21, 2022): 90–97. http://dx.doi.org/10.38109/2225-1685-2022-4-90-97.

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The aim of the work is to evaluate the planarity of the QRS loop and its relationship with systolic dysfunction of the left ventricle in patients in the subacute period of myocardial infarction (MI).Materials and methods. The ECG of 265 patients with a diagnosis of acute myocardial infarction were analyzed. The control group consisted of 55 healthy individuals. The planarity index was calculated as the ratio of the area of the QRS loop projection onto the plane (the polar vector of the QRS loop) and the true area of the QRS loop in space using a synthesized vectorcardiogram.Results. In patients with MI, the planarity index was significantly lower than in healthy individuals: 0,87 [0,71; 0,94] and 0,96 [0,93; 0,97], respectively, p < 0,0001. Weak but significant correlations between the planarity index and the left ventricular ejection fraction (LVEF, r = 0,41, p < 0,001) and with the number of affected segments of the left ventricle according to echocardiography (r = −0,43, p < 0,001) were found. In patients with MI, the planarity index was lower in the presence of pulmonary edema in the acute period of MI (0,68 [0,54; 0,86]; without pulmonary edema 0,88 [0,76; 0,94], p < 0,001), and in the presence of a history of chronic heart failure (0,79 [0,61; 0,88]; without chronic heart failure 0,88 [0,75; 0,94], p = 0,007). In patients with MI of both anterior and inferior localization, the planarity index was significantly lower with LV EF < 50% compared with LV EF ≥ 50%. The planarity index was significantly lower in anterior MI than in inferior MI. Conclusion. In patients in the subacute period of MI, there is a decrease in the QRS loop planarity index, which correlates with the volume of myocardial damage, a decrease in LV EF, and the presence of acute and chronic heart failure. The QRS loop planarity index was significantly lower in anterior MI than in inferior MI.

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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

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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34

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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35

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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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

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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38

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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39

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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40

Fulek, Radoslav, and Csaba D. Tóth. "Atomic Embeddability, Clustered Planarity, and Thickenability." Journal of the ACM 69, no. 2 (April 30, 2022): 1–34. http://dx.doi.org/10.1145/3502264.

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We study the atomic embeddability testing problem, which is a common generalization of clustered planarity ( c-planarity , for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity. C-planarity was introduced in 1995 by Feng, Cohen, and Eades as a variant of graph planarity, in which the vertex set of the input graph is endowed with a hierarchical clustering and we seek an embedding (crossing free drawing) of the graph in the plane that respects the clustering in a certain natural sense. Until now, it has been an open problem whether c-planarity can be tested efficiently. The thickenability problem for simplicial complexes emerged in the topology of manifolds in the 1960s. A 2-dimensional simplicial complex is thickenable if it embeds in some orientable 3-dimensional manifold. Recently, Carmesin announced that thickenability can be tested in polynomial time. Our algorithm for atomic embeddability combines ideas from Carmesin’s work with algorithmic tools previously developed for weak embeddability testing. We express our results purely in terms of graphs on surfaces, and rely on the machinery of topological graph theory. Finally, we give a polynomial-time reduction from atomic embeddability to thickenability thereby showing that both problems are polynomially equivalent, and show that a slight generalization of atomic embeddability to the setting in which clusters are toroidal graphs is NP-complete.

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41

CAIRNS, GRANT, and DANIEL M. ELTON. "THE PLANARITY PROBLEM FOR SIGNED GAUSS WORDS." Journal of Knot Theory and Its Ramifications 02, no. 04 (December 1993): 359–67. http://dx.doi.org/10.1142/s0218216593000209.

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C.F. Gauss gave a necessary condition for a word to be the intersection word of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. M. Dehn provided a solution to the planarity problem [3] and subsequently, different solutions have been given by a number of authors (see [9]). However, all of these solutions are algorithmic in nature. As B. Grünbaum remarked in [7], “they are of the same aesthetically unpleasing character as MacLane’s [1937] criterion for planarity of graphs. A characterization of Gauss codes in the spirit of the Kuratowski criterion for planarity of graphs is still missing”. In this paper we use the work of J. Scott Carter [2] to give a necessary and sufficient condition for planarity of signed Gauss words which is analogous to Gauss’s original condition.

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42

Kwon, Young-Hoo, Noelle J. Tuttle, Cheng-Ju Hung, Nicholas A. Levine, and Seungho Baek. "Linear Relationships Among the Hand and Clubhead Motion Characteristics in Golf Driving in Skilled Male Golfers." Journal of Applied Biomechanics 37, no. 6 (December 1, 2021): 619–28. http://dx.doi.org/10.1123/jab.2021-0303.

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The purpose of this study was to investigate the linear relationships among the hand/clubhead motion characteristics in golf driving in skilled male golfers (n = 66; handicap ≤ 3). The hand motion plane (HMP) and functional swing plane (FSP) angles, the HMP–FSP angle gaps, the planarity characteristics of the off-plane motion of the clubhead, and the attack angles were computed from the drives captured by an optical motion capture system. The HMP angles were identified as the key variables, as the HMP and FSP angles were intercorrelated, but the plane angle gaps, the planarity bias, and the attack angles showed correlations to the HMP angles primarily. Three main swing pattern clusters were identified. The parallel HMP–FSP alignment pattern with a small direction gap was associated with neutral planarity and planar swing pattern. The inward alignment pattern with a large inward direction gap was characterized by flat planes, follow-through-centric planarity, spiral swing pattern, and inward/downward impact. The outward alignment pattern with a large outward direction gap was associated with steep planes, downswing-centric planarity, reverse spiral swing, and outward/upward impact. The findings suggest that practical drills targeting the hand motion pattern can be effective in holistically reprogramming the swing pattern.

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43

Barati, Zahra. "Planarity and outerplanarity indexes of the unit, unitary and total graphs." Filomat 31, no. 9 (2017): 2827–36. http://dx.doi.org/10.2298/fil1709827b.

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In this paper, we consider the problem of planarity and outerplanarity of iterated line graphs of the unit, unitary and total graphs when R is a finite commutative ring. We give a full characterization of all these graphs with respect to their planarity and outerplanarity indexes.

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44

Nikonov, Igor. "A new proof of Vassiliev's conjecture." Journal of Knot Theory and Its Ramifications 23, no. 07 (June 2014): 1460005. http://dx.doi.org/10.1142/s0218216514600050.

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In the paper [First-order invariants and cohomology of spaces of embeddings of self-intersecting curves in ℝn, Izv. Math. 69(5) (2005) 865–912] on finite type invariants of self-intersecting curves, Vassiliev conjectured a criterion of planarity of framed four-valent graphs, i.e. 4-graphs with an opposite edge structure at each vertex. The conjecture was proved by Manturov [A proof of Vassilievs conjecture on the planarity of singular links, Izv. Math. 69(5) (2005) 169–178]. We give here another proof of Vassiliev's planarity criterion of framed four-valent graphs (and more generally, (even) *-graphs), which is based on Pontryagin–Kuratowski theorem.

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45

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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46

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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47

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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48

Truchlewski, A., M. Szczesio, A. Olczak, and M. L. Główka. "Planarity and activity of aroyldithiocarbazoates." Acta Crystallographica Section A Foundations of Crystallography 67, a1 (August 22, 2011): C563. http://dx.doi.org/10.1107/s0108767311085758.

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49

Blanc, Eric, and Włodzimierz Paciorek. "On planarity and similarity restraints." Journal of Applied Crystallography 34, no. 4 (July 22, 2001): 480–83. http://dx.doi.org/10.1107/s0021889801008470.

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Planarity and similarity restraints are described using a unified framework for the computation layout. In both cases, the gradient and Hessian of the restraint residual with respect to atomic coordinates are derived. All computed quantities (residual, gradient, Hessian, normal and distance to the plane for planarity restraints, rotation and translation in the case of similarity) can be obtained directly, without iterative procedure.

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50

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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