Relevant bibliographies by topics / Eulerian graph theory. Hamiltonian graph theory

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Academic literature on the topic 'Eulerian graph theory. Hamiltonian graph theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Eulerian graph theory. Hamiltonian graph theory"

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Tamizh Chelvam, T., and S. Anukumar Kathirvel. "Generalized unit and unitary Cayley graphs of finite rings." Journal of Algebra and Its Applications 18, no. 01 (January 2019): 1950006. http://dx.doi.org/10.1142/s0219498819500063.

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Let [Formula: see text] be a finite commutative ring with nonzero identity and [Formula: see text] be the set of all units of [Formula: see text] The graph [Formula: see text] is the simple undirected graph with vertex set [Formula: see text] in which two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there exists a unit element [Formula: see text] in [Formula: see text] such that [Formula: see text] is a unit in [Formula: see text] In this paper, we obtain degree of all vertices in [Formula: see text] and in turn provide a necessary and sufficient condition for [Formula: see text] to be Eulerian. Also, we give a necessary and sufficient condition for the complement [Formula: see text] to be Eulerian, Hamiltonian and planar.
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Medvedev, Paul, and Mihai Pop. "What do Eulerian and Hamiltonian cycles have to do with genome assembly?" PLOS Computational Biology 17, no. 5 (May 20, 2021): e1008928. http://dx.doi.org/10.1371/journal.pcbi.1008928.

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Many students are taught about genome assembly using the dichotomy between the complexity of finding Eulerian and Hamiltonian cycles (easy versus hard, respectively). This dichotomy is sometimes used to motivate the use of de Bruijn graphs in practice. In this paper, we explain that while de Bruijn graphs have indeed been very useful, the reason has nothing to do with the complexity of the Hamiltonian and Eulerian cycle problems. We give 2 arguments. The first is that a genome reconstruction is never unique and hence an algorithm for finding Eulerian or Hamiltonian cycles is not part of any assembly algorithm used in practice. The second is that even if an arbitrary genome reconstruction was desired, one could do so in linear time in both the Eulerian and Hamiltonian paradigms.
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Metsidik, Metrose. "Eulerian and Even-Face Graph Partial Duals." Symmetry 13, no. 8 (August 11, 2021): 1475. http://dx.doi.org/10.3390/sym13081475.

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Eulerian and bipartite graph is a dual symmetric concept in Graph theory. It is well-known that a plane graph is Eulerian if and only if its geometric dual is bipartite. In this paper, we generalize the well-known result to embedded graphs and partial duals of cellularly embedded graphs, and characterize Eulerian and even-face graph partial duals of a cellularly embedded graph by means of half-edge orientations of its medial graph.
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Broersma, H. J. "A note on K4-closures in hamiltonian graph theory." Discrete Mathematics 121, no. 1-3 (October 1993): 19–23. http://dx.doi.org/10.1016/0012-365x(93)90533-y.

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Broersma, H. J. "On some intriguing problems in hamiltonian graph theory—a survey." Discrete Mathematics 251, no. 1-3 (May 2002): 47–69. http://dx.doi.org/10.1016/s0012-365x(01)00325-9.

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Li, Hao. "Generalizations of Dirac’s theorem in Hamiltonian graph theory—A survey." Discrete Mathematics 313, no. 19 (October 2013): 2034–53. http://dx.doi.org/10.1016/j.disc.2012.11.025.

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Ceulemans, A., E. Lijnen, P. W. Fowler, R. B. Mallion, and T. Pisanski. "Graph theory and the Jahn–Teller theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (November 30, 2011): 971–89. http://dx.doi.org/10.1098/rspa.2011.0508.

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The Jahn–Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex- and edge-weighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons, then degeneracy of states can be resolved by a non-totally symmetric re-weighting of edges and, where necessary, vertices. This leads to the conjecture that whenever the spectrum of a graph contains a set of bonding or anti-bonding degenerate eigenvalues, the roots of the Hamiltonian matrix over this set will show a linear dependence on edge distortions, which has the effect of lifting the degeneracy. When the degenerate level is non-bonding, distortions of vertex weights have to be included to obtain a full resolution of the eigenspace of the degeneracy. Explicit treatments are given for examples of the octahedral graph, where the degeneracy to be lifted is forced by symmetry, and the phenalenyl graph, where the degeneracy is accidental in terms of the automorphism group.
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Blanco, Rocío, and Melody García-Moya. "Graph Theory for Primary School Students with High Skills in Mathematics." Mathematics 9, no. 13 (July 3, 2021): 1567. http://dx.doi.org/10.3390/math9131567.

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Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies.
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Thomassen, Carsten. "On the Number of Hamiltonian Cycles in Bipartite Graphs." Combinatorics, Probability and Computing 5, no. 4 (December 1996): 437–42. http://dx.doi.org/10.1017/s0963548300002182.

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We prove that a bipartite uniquely Hamiltonian graph has a vertex of degree 2 in each color class. As consequences, every bipartite Hamiltonian graph of minimum degree d has at least 21−dd! Hamiltonian cycles, and every bipartite Hamiltonian graph of minimum degree at least 4 and girth g has at least (3/2)g/8 Hamiltonian cycles. We indicate how the existence of more than one Hamiltonian cycle may lead to a general reduction method for Hamiltonian graphs.
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Horák, Peter, Tomáš Kaiser, Moshe Rosenfeld, and Zdeněk Ryjáček. "The Prism Over the Middle-levels Graph is Hamiltonian." Order 22, no. 1 (February 2005): 73–81. http://dx.doi.org/10.1007/s11083-005-9008-7.

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Dissertations / Theses on the topic "Eulerian graph theory. Hamiltonian graph theory"

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Zhan, Mingquan. "Eulerian subgraphs and Hamiltonicity of claw-free graphs." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=3024.

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Thesis (Ph. D.)--West Virginia University, 2003.
Title from document title page. Document formatted into pages; contains vi, 52 p. : ill. Includes abstract. Includes bibliographical references (p. 50-52).
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Dey, Sanjoy. "Structural properties of visibility and weak visibility graphs." Virtual Press, 1997. http://liblink.bsu.edu/uhtbin/catkey/1048394.

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Given a finite set S of n nonintersecting line segments with no three end points collinear, the segment end point visibility graph is defined as the graph whose vertices are the end points of the line segments in S and two vertices are adjacent if the straight line segment joining two end points does not intersect any element of S, or if they are end points of the same segment. Segment end point visibility graphs have a wide variety of applications in VLSI circuit design, study of art gallery problems, and other areas of computational geometry. This thesis contains a survey of the important results that are currently known regarding the characterization of these graphs. Also a weak visibility dual of a segment end point visibility graph is defined and some structural properties of such graphs are presented. Some open problems and questions related to the characterization of weak visibility graphs are also discussed.
Department of Mathematical Sciences
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Smithers, Dayna Brown. "Graph Theory for the Secondary School Classroom." Digital Commons @ East Tennessee State University, 2005. https://dc.etsu.edu/etd/1015.

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After recognizing the beauty and the utility of Graph Theory in solving a variety of problems, the author decided that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in Graph Theory, namely Vertex Coloring, Minimum Spanning Tree, Domination, and Hamiltonian Paths and Cycles, which are appropriate for high school level.
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Steelman, Andrea Elizabeth. "Degree sum ensuring hamiltonicity." [Pensacola, Fla.] : University of West Florida, 2007. http://purl.fcla.edu/fcla/etd/WFE0000012.

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Bajo, Calderon Erica. "An Exploration on the Hamiltonicity of Cayley Digraphs." Youngstown State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ysu161982054497591.

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Vulcani, Renata de Lacerda Martins 1973. "Grafos eulerianos e aplicações." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306826.

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Orientadores: Celia Picinin de Mello, Anamaria Gomide
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-26T19:50:54Z (GMT). No. of bitstreams: 1 Vulcani_RenatadeLacerdaMartins_M.pdf: 2431212 bytes, checksum: 702947f1e783d410ef77eb0234852d6a (MD5) Previous issue date: 2015
Resumo: Neste trabalho apresentamos uma breve introdução à teoria dos grafos, elucidando alguns conceitos básicos e destacando grafos eulerianos. Usamos o conceito de grafos eulerianos para resolver alguns passatempos e jogos conhecidos. Finalizamos apresentando algumas aplicações que envolvem grafos que não são necessariamente eulerianos
Abstract: In this work we present a brief introduction to graph theory, explaining some basic concepts and highlighting eulerians graphs. We use the concept of eulerians graphs to solve some well known puzzles and games. We finalize by presenting some applications involving graphs that are not necessarily eulerians
Mestrado
Matemática em Rede Nacional
Mestra
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Wang, Yinhua. "Fleet assignment, eulerian subtours and extended steiner trees." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/24922.

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Freeman, Andre. "Dual-Eulerian graphs with applications to VLSI design." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-155731/.

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Ghenciu, Petre Ion. "Hamiltonian cycles in subset and subspace graphs." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4662/.

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In this dissertation we study the Hamiltonicity and the uniform-Hamiltonicity of subset graphs, subspace graphs, and their associated bipartite graphs. In 1995 paper "The Subset-Subspace Analogy," Kung states the subspace version of a conjecture. The study of this problem led to a more general class of graphs. Inspired by Clark and Ismail's work in the 1996 paper "Binomial and Q-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and their Q-Analogues," we defined subset graphs, subspace graphs, and their associated bipartite graphs. The main emphasis of this dissertation is to describe those graphs and study their Hamiltonicity. The results on subset graphs are presented in Chapter 3, on subset bipartite graphs in Chapter 4, and on subspace graphs and subspace bipartite graphs in Chapter 5. We conclude the dissertation by suggesting some generalizations of our results concerning the panciclicity of the graphs.
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Fernandes, Antonio M. "A study of nonlinear physical systems in generalized phase space." Virtual Press, 1996. http://liblink.bsu.edu/uhtbin/catkey/1020161.

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Classical mechanics provides a phase space representation of mechanical systems in terms of position and momentum state variables. The Hamiltonian system, a set of partial differential equations, defines a vector field in phase space and uniquely determines the evolutionary process of the system given its initial state.A closed form solution describing system trajectories in phase space is only possible if the system of differential equations defining the Hamiltonian is linear. For nonlinear cases approximate and qualitative methods are required.Generalized phase space methods do not confine state variables to position and momentum, allowing other observables to describe the system. Such a generalization adjusts the description of the system to the required information and provides a method for studying physical systems that are not strictly mechanical.This thesis presents and uses the methods of generalized phase space to compare linear to nonlinear systems.Ball State UniversityMuncie, IN 47306
Department of Physics and Astronomy
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Books on the topic "Eulerian graph theory. Hamiltonian graph theory"

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Fleischner, Herbert. Eulerian graphs and related topics. Amsterdam: North-Holland, 1990.

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Reay, John R. Hamiltonian cycles in t-graphs. New York: Springer-Verlag, 2000.

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Schaar, Günter. Hamiltonian properties of products of graphs and digraphs. Leipzig: Teubner, 1988.

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Kyaw, Shwe. A Dirac-type criterion for hamiltonicity. Berlin: Verlag Köster, 1994.

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Reggini, Horacio C. Regular polyhedra: Random generation, Hamiltonian paths, and single chain nets. Buenos Aires: Academia Nacional de Ciencias Exactas, Físicas y Naturales, 1991.

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Ning, Xuanxi. The blocking flow theory and its application to Hamiltonian graph problems. Aachen: Shaker Verlag, 2006.

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Freĭdlin, M. I. Random perturbations of Hamiltonian systems. Providence, R.I: American Mathematical Society, 1994.

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Filar, Jerzy A. Controlled markov chains, graphs and hamiltonicity. Hanover, Mass: Now Publishers, 2007.

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Cai, Zongxi. Deng zhou wen ti. Beijing: Ke xue chu ban she, 2002.

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Fleischner, Herbert. Eulerian Graphs and Related Topics : Eulerian Graphs and Related Topics. North-Holland, 1991.

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Book chapters on the topic "Eulerian graph theory. Hamiltonian graph theory"

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Balakrishnan, R., and K. Ranganathan. "Eulerian and Hamiltonian Graphs." In A Textbook of Graph Theory, 117–42. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4529-6_6.

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Balakrishnan, R., and K. Ranganathan. "Eulerian and Hamiltonian Graphs." In A Textbook of Graph Theory, 102–27. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8505-7_6.

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Zhang, Ping. "Hamiltonian Extension." In Graph Theory, 17–30. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31940-7_2.

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Bantva, Devsi, and S. K. Vaidya. "Hamiltonian Chromatic Number of Trees." In Recent Advancements in Graph Theory, 339–52. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-28.

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Golumbic, Martin Charles, and André Sainte-Laguë. "VII Hamiltonian graphs." In The Zeroth Book of Graph Theory, 51–60. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61420-1_8.

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Thaithae, Sermsri, and Narong Punnim. "The Hamiltonian Number of Cubic Graphs." In Computational Geometry and Graph Theory, 213–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89550-3_23.

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Matsuda, Haruhide. "Regular Factors Containing a Given Hamiltonian Cycle." In Combinatorial Geometry and Graph Theory, 123–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-30540-8_14.

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Bauer, D., H. J. Broersma, and H. J. Veldman. "Around Three Lemmas in Hamiltonian Graph Theory." In Topics in Combinatorics and Graph Theory, 101–10. Heidelberg: Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_12.

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Ray, Saha. "Euler Graphs and Hamiltonian Graphs." In Graph Theory with Algorithms and its Applications, 25–34. India: Springer India, 2012. http://dx.doi.org/10.1007/978-81-322-0750-4_3.

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Momège, Benjamin. "Sufficient Conditions for a Connected Graph to Have a Hamiltonian Path." In SOFSEM 2017: Theory and Practice of Computer Science, 205–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51963-0_16.

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Conference papers on the topic "Eulerian graph theory. Hamiltonian graph theory"

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Vontobel, Pascal O. "A factor-graph approach to Lagrangian and Hamiltonian dynamics." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6033945.

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Onete, Cristian E., and A. Maria Cristina C. Onete. "Finding spanning trees and Hamiltonian circuits in an un-oriented graph an algebraic approach." In 2011 European Conference on Circuit Theory and Design (ECCTD). IEEE, 2011. http://dx.doi.org/10.1109/ecctd.2011.6043384.

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Gasparetto, A., R. Vidoni, E. Saccavini, and D. Pillan. "Optimal Path Planning for Painting Robots." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24259.

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In this work, a robotic painting task is addressed in order to automate and improve the efficiency of the process. Usually, path planning in robotic painting is done through self learning programming. Recently, different automated and semi-automated systems have been developed in order to avoid this procedure by using a CAD-drawing to create a CAD-guided trajectory for the paint gun, or by acquiring and recognizing the overall shape of the object to be painted within a library of prestored shapes with associated pre-defined paths. However, a general solution is still lacking, which enables one to overcome the need for a CAD-drawing and to deal with any kind of shapes. In this paper, graph theory and operative research techniques are applied to provide a general and optimal solution of the path planning problem for painting robots. The object to be painted is partitioned into primitives that can be represented by a graph. The Chinese Postman algorithm is then run on the graph in order to obtain a minimum length path covering all the arcs (Eulerian path). However, this path is not always optimal with respect to the constraints imposed by the painting process, hence dedicated algorithms have been developed in order to generate the optimal path in such cases. Based on the optimal path, the robot trajectories are planned by imposing a constant velocity motion of the spray gun, in order to ensure a uniform distribution of the paint over the object surface. The proposed system for optimal path planning has been implemented in a Matlab environment and extensively tested with excellent results in terms of time, costs and usability.
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