Towards A Theory Of Geometric Graphs

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Towards a Theory of Geometric Graphs

Author : János Pach
Publisher : American Mathematical Soc.
ISBN 13 : 0821834843
Total Pages : 283 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Towards a Theory of Geometric Graphs by : János Pach

Download or read book Towards a Theory of Geometric Graphs written by János Pach and published by American Mathematical Soc.. This book was released on 2004 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graphs and Geometry

Author : László Lovász
Publisher : American Mathematical Soc.
ISBN 13 : 1470450879
Total Pages : 444 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Graphs and Geometry by : László Lovász

Download or read book Graphs and Geometry written by László Lovász and published by American Mathematical Soc.. This book was released on 2019-08-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.

Thirty Essays on Geometric Graph Theory

Author : János Pach
Publisher : Springer Science & Business Media
ISBN 13 : 1461401100
Total Pages : 610 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Thirty Essays on Geometric Graph Theory by : János Pach

Download or read book Thirty Essays on Geometric Graph Theory written by János Pach and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Graphs and Arrangements

Author : Stefan Felsner
Publisher : Springer Science & Business Media
ISBN 13 : 3322803031
Total Pages : 179 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Geometric Graphs and Arrangements by : Stefan Felsner

Download or read book Geometric Graphs and Arrangements written by Stefan Felsner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Geometric Graphs

Author : Mathew Penrose
Publisher : Oxford University Press
ISBN 13 : 0198506260
Total Pages : 345 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Random Geometric Graphs by : Mathew Penrose

Download or read book Random Geometric Graphs written by Mathew Penrose and published by Oxford University Press. This book was released on 2003 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides and explains the mathematics behind geometric graph theory, which studies the properties of a graph that consists of nodes placed in Euclidean space so that edges can be added to connect points that are close to one another. For example, a collection of trees scattered in a forest and the disease that is passed between them, a set of nests of animals or birds on a region and the communication between them or communication between communications stations or nerve cells. Aimed at graduate students and researchers in probability, statistics, combinatorics and graph theory including computer scientists, it covers topics such as: technical tools, edge and component counts, vertex degrees, clique and chromatic number, and connectivity. Applications of this theory are used in the study of neural networks, spread of disease, astrophysics and spatial statistics.

Erdös Centennial

Author : László Lovász
Publisher : Springer Science & Business Media
ISBN 13 : 3642392865
Total Pages : 720 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Erdös Centennial by : László Lovász

Download or read book Erdös Centennial written by László Lovász and published by Springer Science & Business Media. This book was released on 2014-01-24 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.

Analysis and Geometry on Graphs and Manifolds

Author : Matthias Keller
Publisher : Cambridge University Press
ISBN 13 : 1108587380
Total Pages : 493 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Analysis and Geometry on Graphs and Manifolds by : Matthias Keller

Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.

Geometric Group Theory

Author : Clara Löh
Publisher : Springer
ISBN 13 : 3319722549
Total Pages : 389 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Geometric Group Theory by : Clara Löh

Download or read book Geometric Group Theory written by Clara Löh and published by Springer. This book was released on 2017-12-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Combinatorial Geometry and Graph Theory

Author : Jin Akiyama
Publisher : Springer
ISBN 13 : 3540305408
Total Pages : 227 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Combinatorial Geometry and Graph Theory by : Jin Akiyama

Download or read book Combinatorial Geometry and Graph Theory written by Jin Akiyama and published by Springer. This book was released on 2005-01-18 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003, held in Bandung, Indonesia in September 2003. The 23 revised papers presented were carefully selected during two rounds of reviewing and improvement. Among the topics covered are coverings, convex polygons, convex polyhedra, matchings, graph colourings, crossing numbers, subdivision numbers, combinatorial optimization, combinatorics, spanning trees, various graph characteristica, convex bodies, labelling, Ramsey number estimation, etc.

Discrete Geometry, Combinatorics and Graph Theory

Author : Jin Akiyama
Publisher : Springer
ISBN 13 : 3540706666
Total Pages : 289 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Discrete Geometry, Combinatorics and Graph Theory by : Jin Akiyama

Download or read book Discrete Geometry, Combinatorics and Graph Theory written by Jin Akiyama and published by Springer. This book was released on 2007-06-26 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi'an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.

More Sets, Graphs and Numbers

Author : Ervin Gyori
Publisher : Springer Science & Business Media
ISBN 13 : 3540324399
Total Pages : 399 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis More Sets, Graphs and Numbers by : Ervin Gyori

Download or read book More Sets, Graphs and Numbers written by Ervin Gyori and published by Springer Science & Business Media. This book was released on 2010-10-02 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.

Topological Crystallography

Author : Toshikazu Sunada
Publisher : Springer Science & Business Media
ISBN 13 : 4431541772
Total Pages : 229 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Topological Crystallography by : Toshikazu Sunada

Download or read book Topological Crystallography written by Toshikazu Sunada and published by Springer Science & Business Media. This book was released on 2012-12-23 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.

Geometric Set Theory

Author : Paul B. Larson
Publisher : American Mathematical Soc.
ISBN 13 : 1470454629
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric Set Theory by : Paul B. Larson

Download or read book Geometric Set Theory written by Paul B. Larson and published by American Mathematical Soc.. This book was released on 2020-07-16 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

SOFSEM 2005: Theory and Practice of Computer Science

Author : Maria Bieliková
Publisher : Springer Science & Business Media
ISBN 13 : 354024302X
Total Pages : 442 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis SOFSEM 2005: Theory and Practice of Computer Science by : Maria Bieliková

Download or read book SOFSEM 2005: Theory and Practice of Computer Science written by Maria Bieliková and published by Springer Science & Business Media. This book was released on 2005-01-27 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 31st Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2005, held in Liptovský Ján, Slovakia in January 2005. The 28 revised full papers and 16 revised short papers presented together with 8 invited contributions were carefully reviewed and selected from 144 submissions. The papers were organized in four topical tracks on foundations of computer science, modeling and searching data in the web area, software engineering, and graph drawing and discrete computational mathematics.

Handbook of Graph Drawing and Visualization

Author : Roberto Tamassia
Publisher : CRC Press
ISBN 13 : 1584884126
Total Pages : 869 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Handbook of Graph Drawing and Visualization by : Roberto Tamassia

Download or read book Handbook of Graph Drawing and Visualization written by Roberto Tamassia and published by CRC Press. This book was released on 2013-08-19 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references. The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks. Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.

Graph Theory As I Have Known It

Author : W. T. Tutte
Publisher : Clarendon Press
ISBN 13 : 0191637785
Total Pages : 164 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Graph Theory As I Have Known It by : W. T. Tutte

Download or read book Graph Theory As I Have Known It written by W. T. Tutte and published by Clarendon Press. This book was released on 2012-05-24 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as comnbinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.

Crossing Numbers of Graphs

Author : Marcus Schaefer
Publisher : CRC Press
ISBN 13 : 1351648446
Total Pages : 281 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Crossing Numbers of Graphs by : Marcus Schaefer

Download or read book Crossing Numbers of Graphs written by Marcus Schaefer and published by CRC Press. This book was released on 2018-01-02 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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