Towards A Theory Of Geometric Graphs

Author : János Pach
Publisher : American Mathematical Soc.
ISBN 13 : 0821834843
Total Pages : 300 pages
Book Rating : 4.48/5 ( download)

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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 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on graph theory, with the common theme that all the graph theoretical problems addressed are approached from a geometrical, rather than an abstract point of view. This is no accident; the editor selected these papers not as a comprehensive literature revie

Author : László Lovász
Publisher : American Mathematical Soc.
ISBN 13 : 1470450879
Total Pages : 444 pages
Book Rating : 4.78/5 ( download)

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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.

Author : Stefan Felsner
Publisher : Springer Science & Business Media
ISBN 13 : 3322803031
Total Pages : 179 pages
Book Rating : 4.30/5 ( download)

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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.

Author : János Pach
Publisher : Springer Science & Business Media
ISBN 13 : 1461401100
Total Pages : 610 pages
Book Rating : 4.00/5 ( download)

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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.

Author : Mathew Penrose
Publisher : Oxford University Press
ISBN 13 : 0198506260
Total Pages : 345 pages
Book Rating : 4.63/5 ( download)

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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.

Author : Matthias Keller
Publisher : Cambridge University Press
ISBN 13 : 1108587380
Total Pages : 493 pages
Book Rating : 4.89/5 ( download)

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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.

Author : Toshikazu Sunada
Publisher : Springer Science & Business Media
ISBN 13 : 4431541772
Total Pages : 236 pages
Book Rating : 4.76/5 ( download)

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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 236 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.

Author : László Lovász
Publisher : Springer Science & Business Media
ISBN 13 : 3642392865
Total Pages : 714 pages
Book Rating : 4.63/5 ( download)

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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 714 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.

Author : Clara Löh
Publisher : Springer
ISBN 13 : 3319722549
Total Pages : 389 pages
Book Rating : 4.42/5 ( download)

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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.

Author : Jin Akiyama
Publisher : Springer
ISBN 13 : 3540305408
Total Pages : 234 pages
Book Rating : 4.08/5 ( download)

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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 234 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.