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Author: Vadim Zverovich
Publisher: Oxford University Press
ISBN: 0198882106
Category : Mathematics
Languages : en
Pages : 289
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Book Description
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Author: Vadim Zverovich
Publisher: Oxford University Press
ISBN: 0198882106
Category : Mathematics
Languages : en
Pages : 289
Get Book Here
Book Description
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Author: Jomon Kottarathil
Publisher: CRC Press
ISBN: 1040018734
Category : Mathematics
Languages : en
Pages : 201
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Book Description
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.
Author: Reinhard Diestel
Publisher: Oxford Science Publications
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 258
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Book Description
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible ofresearch in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems.Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
Author: Fan Chung
Publisher: CRC Press
ISBN: 1000752097
Category : Mathematics
Languages : en
Pages : 410
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Book Description
50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter
Author: Michael Kaufmann
Publisher: Springer
ISBN: 3540709045
Category : Computers
Languages : en
Pages : 466
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the 14th International Symposium on Graph Drawing, GD 2006, held in Karlsruhe, Germany. The 33 revised full papers and 5 revised short papers presented together with 2 invited talks, 1 system demo, 2 poster papers address all current aspects in graph drawing, ranging from foundational and methodological issues to applications for various classes of graphs in a variety of fields.
Author: Jan van Leeuwen
Publisher: Springer Science & Business Media
ISBN: 9783540578994
Category : Computers
Languages : en
Pages : 452
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Book Description
This volume contains the proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science, WG '93, held near Utrecht, The Netherlands, in 1993. The papers are grouped into parts on: hard problems on classes of graphs, structural graph theory, dynamic graph algorithms, structure-oriented graph algorithms, graph coloring, AT-free and chordal graphs, circuits and nets, graphs and interconnection networks, routing and shortest paths, and graph embedding and layout. The 35 revised papers were chosen from 92 submissions after a careful refereeing process.
Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 3540241329
Category : Computers
Languages : en
Pages : 413
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the 30th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2004, held in Bad Honnef, Germany in June 2004. The 31 revised full papers presented together with 2 invited papers were carefully selected from 66 submissions during two rounds of reviewing and improvement. The papers are organized in topical sections on graph algorithms: trees; graph algorithms: recognition and decomposition; graph algorithms: various problems; optimization and approximation algorithms; parameterized complexity and exponential algorithms; counting, combinatorics, and optimization; applications in bioinformatics and graph drawing; and graph classes and NP-hard problems.
Author: N.B. Singh
Publisher: N.B. Singh
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
"Combinatorial Problems in Graph Theory" offers a comprehensive introduction to the fundamentals of graph theory for beginners. Exploring the fascinating world of graphs, this book covers essential concepts, from basic definitions to advanced applications across diverse fields such as computer science, optimization, and social networks. With clear explanations, practical examples, and engaging problems, it equips readers with the foundational knowledge needed to understand and solve combinatorial problems using graph theory. Ideal for students and enthusiasts alike, this book serves as an accessible entry point into this essential branch of mathematics.
Author: R. Diestel
Publisher: Elsevier
ISBN: 148329479X
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.
Author: Reinhard Diestel
Publisher: Springer (print edition); Reinhard Diestel (eBooks)
ISBN:
Category : Mathematics
Languages : en
Pages : 472
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Book Description
Professional electronic edition, and student eBook edition (freely installable PDF with navigational links), available from diestel-graph-theory.com This standard textbook of modern graph theory, now in its sixth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. New in this 6th edition: Two new sections on how to apply the regularity lemma: counting lemma, removal lemma, and Szemerédi's theorem. New chapter section on chi-boundedness. Gallai's A-paths theorem. New or substantially simplified proofs of: - Lovász's perfect graph theorem - Seymour's 6-flow theorem - Turán's theorem - Tutte's theorem about flow polynomials - the Chvátal-Erdös theorem on Hamilton cycles - the tree-of-tangles theorem for graph minors (two new proofs, one canonical) - the 5-colour theorem Several new proofs of classical theorems. Many new exercises. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.” Acta Scientiarum Mathematicarum "Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity." Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory.” Bulletin of the Institute of Combinatorics and its Applications “Succeeds dramatically… a hell of a good book.” MAA Reviews “A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors.” Mathematika “…like listening to someone explain mathematics.” Bulletin of the AMS
