Thirty Essays on Geometric Graph Theory PDF Download

Author: János Pach
Publisher: Springer Science & Business Media
ISBN: 1461401100
Category : Mathematics
Languages : en
Pages : 610

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Book Description
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.

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: 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: Jonathan L. Gross
Publisher: CRC Press
ISBN: 1439880190
Category : Mathematics
Languages : en
Pages : 1630

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Book Description
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Author: Jaroslav Nešetřil
Publisher: Springer Science & Business Media
ISBN: 887642475X
Category : Mathematics
Languages : en
Pages : 600

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Book Description
In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.

Author: David Auber
Publisher: Springer Nature
ISBN: 303068766X
Category : Computers
Languages : en
Pages : 546

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Book Description
This book constitutes the refereed proceedings of the 28th International Symposium on Graph Drawing and Network Visualization, GD 2020, which was held during September 16-18, 2020. The conference was planned to take place in Vancouver, Canada, but changed to an online format due to the COVID-19 pandemic. The 29 full and 9 short papers presented in this volume were carefully reviewed and selected from 82 submissions. They were organized in topical sections named: gradient descent and queue layouts; drawing tree-like graphs, visualization, and special drawings of elementary graphs; restricted drawings of special graph classes; orthogonality; topological constraints; crossings, k-planar graphs; planarity; graphs drawing contest.

Author: Christian Duncan
Publisher: Springer
ISBN: 3662458039
Category : Computers
Languages : en
Pages : 530

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Book Description
This book constitutes the proceedings of the 22nd International Symposium on Graph Drawing, GD 2014, held in Würzburg, Germany, in September 2014. The 41 full papers presented in this volume were carefully reviewed and selected from 72 submissions. The back matter of the book also contains 2 page poster papers presented at the conference. The contributions are organized in topical sections named: planar subgraphs; simultaneous embeddings; applications; contact representations; k-planar graphs; crossing minimization; level drawings; theory; fixed edge directions; drawing under constraints; clustered planarity; and greedy graphs.

Author: Stephen Wismath
Publisher: Springer
ISBN: 3319038419
Category : Computers
Languages : en
Pages : 540

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Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 21st International Symposium on Graph Drawing, GD 2013, held in Bordeaux, France, in September 2013. The 42 revised full papers presented together with 12 revised short papers, 3 invited talks and 1 poster description were carefully reviewed and selected from 110 submissions. The papers are organized in topical sections on upward drawings, planarity, beyond planarity, geometric representations, 3D et al., universality, practical graph drawing, subgraphs, crossings, geometric graphs and geographic networks, angular restrictions, grids, curves and routes. The book also contains a short description of the graph drawing contest.

Author: Michael A. Bekos
Publisher: Springer Nature
ISBN: 3031492722
Category : Computers
Languages : en
Pages : 368

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Book Description
This two-volume set LNCS 14465-14466 constitutes the proceedings of the 31st International Symposium on Graph Drawing and Network Visualization, GD 2023, held in Isola delle Femmine, Palermo, Italy, in September 2023. The 31 full papers, 7 short papers, presented together with 2 invited talks, and one contest report, were thoroughly reviewed and selected from the 100 submissions. The abstracts of 11 posters presented at the conference can be found in the back matter of the volume. The contributions were organized in topical sections as follows: beyond planarity; crossing numbers; linear layouts; geometric aspects; visualization challenges; graph representations; graph decompositions; topological aspects; parameterized complexity for drawings; planar graphs; frameworks; algorithmics.

Author: Marcus Schaefer
Publisher: CRC Press
ISBN: 1351648446
Category : Mathematics
Languages : en
Pages : 281

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Book Description
Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers