Graph Theory As I Have Known It

Author: W. T. Tutte
Publisher: Oxford University Press on Demand
ISBN: 0199660557
Size: 47.56 MB
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A unique introduction to graph theory, written by one of the founding fathers. Professor William Tutte, codebreaker and mathematician, details his experiences in the area and provides a fascinating insight into the processes leading to his proofs.

Connections In Combinatorial Optimization

Author: András Frank
Publisher: OUP Oxford
ISBN: 0199205272
Size: 43.83 MB
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Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.

Phylogenetics

Author: Charles Semple
Publisher: Oxford University Press on Demand
ISBN: 9780198509424
Size: 51.59 MB
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Phylogenetic trees and networks are widely used throughout evolutionary biology, epidemiology, and ecology to infer the historical relationships between species through inherited characteristics. This work discusses the mathematics that underlies the reconstruction and analysis of these phylogenetic trees.

Fast Parallel Algorithms For Graph Matching Problems

Author: Marek Karpiński
Publisher: Oxford University Press
ISBN: 9780198501626
Size: 37.39 MB
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The matching problem is one of the central problems in graph theory as well as in the theory of algorithms and their applications. This book will provide the reader with a comprehensive and straightforward introduction to the basic methods of designing efficient parallel algorithms for graph matching problems. The text is written for students at the beginning graduate level. The exposition is mostly self-contained and example-driven. Prerequisites have been kept to a minimum by includingrelevant background material. The book contains full details of several new techniques and should also be of interest to research workers in computer science, operations research, discrete mathematics, and electrical engineering. The main theoretical tools are combined into three independent chapters, devoted to combinatorial tools, probabilistic tools, and algebraic tools. One of the main goals of the book is to bring together these three approaches and highlight how their combination worksin the development of efficient parallel algorithms. The reader will be provided with a simple and transparent presentation of a variety of interesting algorithms, including many examples and illustrations. The combination of different approaches makes the matching problem and its applications an attractive and fascinating subject. It is hoped that the book represents a meeting point of interesting algorithmic techniques and opens up new algebraic and geometric areas. Marek Karpinski is Chair Professor of Computer Science at the University of Bonn. Wojciech Rytter is Professor of Computer Science at the University of Warsaw and at the University of Liverpool.

Algorithms On Trees And Graphs

Author: Gabriel Valiente
Publisher: Springer Science & Business Media
ISBN: 366204921X
Size: 35.70 MB
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Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, such as approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms.

Graph Connections

Author: Lowell W. Beineke
Publisher: Oxford University Press on Demand
ISBN:
Size: 39.93 MB
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The purpose of this book is to inform mathematicians about the applicability of graph theory to other areas of mathematics, from number theory, to linear algebra, knots, neural networks, and finance. This is achieved through a series of expository chapters, each devoted to a different field and written by an expert in that field. This book is more than a collection of essays however, in that the chapters have been carefully edited to ensure a common level of exposition, with terminology and notation standardized as far as possible. This book will be useful to professsional mathematicians and graduate students. It should also appeal to scientists working in other areas.

Topics On Analysis In Metric Spaces

Author: Luigi Ambrosio
Publisher: Oxford University Press on Demand
ISBN: 9780198529385
Size: 18.21 MB
Format: PDF, ePub, Mobi
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This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

Graphs And Homomorphisms

Author: Pavol Hell
Publisher: OUP Oxford
ISBN: 0198528175
Size: 23.72 MB
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This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level and has been used for courses at Simon Fraser University (Vancouver), Charles University (Prague), ETH (Zurich), and UFRJ (Rio de Janeiro).The exercises vary in difficulty. The first few are usually intended to give the reader an opportunity to practice the concepts introduced in the chapter; the later ones explore related concepts, or even introduce new ones. For the harder exercises hints and references are provided.The authors are well known for their research in this area and the book will be invaluable to graduate students and researchers alike.