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The Decline And Fall Of Zarankiewicz S Theorem

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Graph And Network Theory

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Author : Michael A. Henning
language : en
Publisher: Springer Nature
Release Date : 2022-06-03

Graph And Network Theory written by Michael A. Henning and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-03 with Business & Economics categories.

This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.

Topics In Topological Graph Theory

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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09

Topics In Topological Graph Theory written by Lowell W. Beineke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Mathematics categories.

The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.

Handbook Of Graph Theory Second Edition

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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2013-12-17

Handbook Of Graph Theory Second Edition written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Mathematics categories.

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.

Handbook Of Discrete And Computational Geometry

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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22

Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.

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.

Handbook Of Combinatorics Volume 1

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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 1995-12-11

Handbook Of Combinatorics Volume 1 written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Computers categories.

Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.

Efficient Algorithms

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Author : Helmut Alt
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-28

Efficient Algorithms written by Helmut Alt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-28 with Computers categories.

This Festschrift volume, published in honor of Kurt Mehlhorn on the occasion of his 60th birthday, contains 28 papers written by his former Ph.D. students and colleagues as well as by his former Ph.D. advisor, Bob Constable. The volume's title is a translation of the title of Kurt Mehlhorn's first book, "Effiziente Algorithmen", published by Teubner-Verlag in 1977. This Festschrift demonstrates how the field of algorithmics has developed and matured in the decades since then. The papers included in this volume are organized in topical sections on models of computation and complexity; sorting and searching; combinatorial optimization with applications; computational geometry and geometric graphs; and algorithm engineering, exactness and robustness.

Handbook Of Combinatorics Volume 1

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Author : Ronald L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11

Handbook Of Combinatorics Volume 1 written by Ronald L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Business & Economics categories.

Handbook Of Discrete And Computational Geometry Second Edition

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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2004-04-13

Handbook Of Discrete And Computational Geometry Second Edition written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-13 with Mathematics categories.

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

Handbook Of Combinatorics

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Author : R.L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11

Handbook Of Combinatorics written by R.L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Computers categories.

Handbook of Combinatorics

Handbook Of Combinatorics

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Author : Ronald L. Graham
language : en
Publisher: MIT Press
Release Date : 2003-03

Handbook Of Combinatorics written by Ronald L. Graham and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03 with Computers categories.

Covers combinatorics in graph theory, theoretical computer science, optimization, and convexity theory, plus applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science.

The Decline And Fall Of Zarankiewicz S Theorem

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