Exercises In Graph Theory
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Exercises In Graph Theory
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Author : O. Melnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Exercises In Graph Theory written by O. Melnikov 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 2013-04-18 with Mathematics categories.
This book supplements the textbook of the authors" Lectures on Graph The ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord ing to the topics of graph theory: paths, cycles, components, subgraphs, re constructibility, operations on graphs, graphs and matrices, trees, independence, matchings, coverings, connectivity, matroids, planarity, Eulerian and Hamiltonian graphs, degree sequences, colorings, digraphs, hypergraphs. Each section starts with main definitions and brief theoretical discussions. They constitute a minimal background, just a reminder, for solving the exercises. the presented facts and a more extended exposition may be found in Proofs of the mentioned textbook of the authors, as well as in many other books in graph theory. Most exercises are supplied with answers and hints. In many cases complete solutions are given. At the end of the book you may find the index of terms and the glossary of notations. The "Bibliography" list refers only to the books used by the authors during the preparation of the exercisebook. Clearly, it mentions only a fraction of available books in graph theory. The invention of the authors was also driven by numerous journal articles, which are impossible to list here.
Combinatorial Problems And Exercises
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Author : L. Lovász
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Combinatorial Problems And Exercises written by L. Lovász and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
Graphs Theory And Applications
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Author : Jean-Claude Fournier
language : en
Publisher: John Wiley & Sons
Release Date : 2013-05-06
Graphs Theory And Applications written by Jean-Claude Fournier and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-06 with Mathematics categories.
This book provides a comprehensive and pedagogical introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the travelling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications.
Graph Theory And Its Applications
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2018-11-05
Graph Theory And Its Applications 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 2018-11-05 with Computers categories.
Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.
A Beginner S Guide To Graph Theory
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Author : W.D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-05
A Beginner S Guide To Graph Theory written by W.D. Wallis 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 2010-05-05 with Mathematics categories.
Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use
A Walk Through Combinatorics
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Author : Miklós Bóna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-09-15
A Walk Through Combinatorics written by Miklós Bóna and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-15 with Mathematics categories.
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity. The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]. The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
A First Course In Graph Theory
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Author : Gary Chartrand
language : en
Publisher: Courier Corporation
Release Date : 2013-05-20
A First Course In Graph Theory written by Gary Chartrand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Graph Theory And Its Applications Second Edition
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2005-09-22
Graph Theory And Its Applications 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 2005-09-22 with Mathematics categories.
Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
A Walk Through Combinatorics
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Author : Mikl¢s B¢na
language : en
Publisher: World Scientific
Release Date : 2006
A Walk Through Combinatorics written by Mikl¢s B¢na and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
The Fascinating World Of Graph Theory
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Author : Arthur Benjamin
language : en
Publisher: Princeton University Press
Release Date : 2017-06-06
The Fascinating World Of Graph Theory written by Arthur Benjamin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-06 with Mathematics categories.
The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.