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Author: Stefan Felsner
Publisher: Springer Science & Business Media
ISBN: 3322803031
Category : Mathematics
Languages : en
Pages : 179
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Book Description
Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Author: Stefan Felsner
Publisher: Springer Science & Business Media
ISBN: 3322803031
Category : Mathematics
Languages : en
Pages : 179
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Book Description
Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Author: Stefan Felsner
Publisher:
ISBN: 9783322803047
Category :
Languages : en
Pages : 184
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Book Description
Author: János Pach
Publisher: American Mathematical Soc.
ISBN: 0821834843
Category : Mathematics
Languages : en
Pages : 283
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Book Description
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical ""Theory of Finite and Infinite Graphs"", the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects.Many of the powerful techniques developed in these fields have been successfully applied in other areas of mathematics. However, the same methods were often incapable of providing satisfactory answers to questions arising in geometric applications. In the spirit of Konig, geometric graph theory focuses on combinatorial and geometric properties of graphs drawn in the plane by straight-line edges (or more generally, by edges represented by simple Jordan arcs). It is an emerging discipline that abounds in open problems, but it has already yielded some striking results which have proved instrumental in the solution of several basic problems in combinatorial and computational geometry. The present volume is a careful selection of 25 invited and thoroughly refereed papers, reporting about important recent discoveries on the way Towards a Theory of Geometric Graphs.
Author: Ezra Miller
Publisher: American Mathematical Soc.
ISBN: 0821837362
Category : Combinatorial analysis
Languages : en
Pages : 705
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Book Description
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
Author: János Pach
Publisher: John Wiley & Sons
ISBN: 1118031369
Category : Mathematics
Languages : en
Pages : 376
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Book Description
A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more
Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1498711421
Category : Computers
Languages : en
Pages : 1928
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Book Description
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Author: Andras Bezdek
Publisher: CRC Press
ISBN: 0824747615
Category : Mathematics
Languages : en
Pages : 500
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Book Description
Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.
Author: Daniel Archambault
Publisher: Springer Nature
ISBN: 303035802X
Category : Computers
Languages : en
Pages : 624
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Book Description
This book constitutes the refereed proceedings of the 27th International Symposium on Graph Drawing and Network Visualization, GD 2019, held in Prague, Czech Republic, in September 2019. The 42 papers and 12 posters presented in this volume were carefully reviewed and selected from 113 submissions. They were organized into the following topical sections: Cartograms and Intersection Graphs, Geometric Graph Theory, Clustering, Quality Metrics, Arrangements, A Low Number of Crossings, Best Paper in Track 1, Morphing and Planarity, Parameterized Complexity, Collinearities, Topological Graph Theory, Best Paper in Track 2, Level Planarity, Graph Drawing Contest Report, and Poster Abstracts.
Author: B. Gr\unbaum"
Publisher: American Mathematical Soc.
ISBN: 0821888609
Category :
Languages : en
Pages : 122
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Book Description
Author: Emilio Di Giacomo
Publisher: Springer
ISBN: 3319272616
Category : Computers
Languages : en
Pages : 566
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Book Description
This book constitutes the proceedings of the 23rd International Symposium on Graph Drawing and Network Visualization, GD 2015, held in Los Angeles, Ca, USA, in September 2015. The 35 full papers presented together with 7 short papers and 8 posters in this volume were carefully reviewed and selected from 77 submissions. Graph Drawing is concerned with the geometric representation of graphs and constitutes the algorithmic core of Network Visualization. Graph Drawing and Network Visualization are motivated by applications where it is crucial to visually analyze and interact with relational datasets. Examples of such application areas include social sciences, Internet and Web computing, information systems, computational biology, networking, VLSI circuit design, and software engineering. This year the Steering Committee of GD decided to extend the name of the conference from the "International Symposium on Graph Drawing" to the "International Symposium on Graph Drawing and Network Visualization" in order to better emphasize the dual focus of the conference on combinatorial and algorithmic aspects as well as the design of network visualization systems and interfaces.
