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Hypergraph Theory

Hypergraph Theory PDF Author: Alain Bretto
Publisher: Springer Science & Business Media
ISBN: 3319000802
Category : Mathematics
Languages : en
Pages : 119

Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.

Hypergraph Theory

Hypergraph Theory PDF Author: Alain Bretto
Publisher: Springer Science & Business Media
ISBN: 3319000802
Category : Mathematics
Languages : en
Pages : 119

Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.

Hypergraph Theory

Hypergraph Theory PDF Author: Alain Bretto
Publisher: Springer
ISBN: 9783319033709
Category : Mathematics
Languages : en
Pages : 0

Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.

Coloring Mixed Hypergraphs: Theory, Algorithms and Applications

Coloring Mixed Hypergraphs: Theory, Algorithms and Applications PDF Author: Vitaly Ivanovich Voloshin
Publisher: American Mathematical Soc.
ISBN: 0821828126
Category : Hypergraphs
Languages : en
Pages : 199

Book Description
The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.

Hypergraphs and Designs

Hypergraphs and Designs PDF Author: Mario Gionfriddo
Publisher: Nova Science Publishers
ISBN: 9781633219113
Category : Hypergraphs
Languages : en
Pages : 0

Book Description
Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorisations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well-developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be "Combinatorial designs as hypergraphs". There is no analogue to this book on the market. Its primary audience is researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects.

Hypergraphs

Hypergraphs PDF Author: C. Berge
Publisher: Elsevier
ISBN: 0080880231
Category : Mathematics
Languages : en
Pages : 267

Book Description
Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.

Hypergraph Theory in Wireless Communication Networks

Hypergraph Theory in Wireless Communication Networks PDF Author: Hongliang Zhang
Publisher: Springer
ISBN: 3319604694
Category : Technology & Engineering
Languages : en
Pages : 62

Book Description
This brief focuses on introducing a novel mathematical framework, referred as hypergraph theory, to model and solve the multiple interferer scenarios for future wireless communication networks. First, in Chap. 1, the authors introduce the basic preliminaries of hypergraph theory in general, and develop two hypergraph based polynomial algorithms, i.e., hypergraph coloring and hypergraph clustering. Then, in Chaps. 2 and 3, the authors present two emerging applications of hypergraph coloring and hypergraph clustering in Device-to-Device (D2D) underlay communication networks, respectively, in order to show the advantages of hypergraph theory compared with the traditional graph theory. Finally, in Chap. 4, the authors discuss the limitations of using hypergraph theory in future wireless networks and briefly present some other potential applications. This brief introduces the state-of-the-art research on the hypergraph theory and its applications in wireless communications. An efficient framework is provided for the researchers, professionals and advanced level students who are interested in the radio resource allocation in the heterogeneous networks to solve the resource allocation and interference management problems.

Applications of Hyperstructure Theory

Applications of Hyperstructure Theory PDF Author: P. Corsini
Publisher: Springer Science & Business Media
ISBN: 1475737149
Category : Mathematics
Languages : en
Pages : 333

Book Description
This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.

Fractional Graph Theory

Fractional Graph Theory PDF Author: Edward R. Scheinerman
Publisher: Courier Corporation
ISBN: 0486292134
Category : Mathematics
Languages : en
Pages : 240

Book Description
This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.

Tensor Analysis

Tensor Analysis PDF Author: Liqun Qi
Publisher: SIAM
ISBN: 1611974747
Category : Mathematics
Languages : en
Pages : 313

Book Description
Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?

An Irregular Mind

An Irregular Mind PDF Author: Imre Bárány
Publisher: Springer Science & Business Media
ISBN: 3642144446
Category : Mathematics
Languages : en
Pages : 749

Book Description
Szemerédi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of Szemerédi's achievements and personality, on the occasion of his seventieth birthday. It exemplifies his extraordinary vision and unique way of thinking. A number of colleagues and friends, all top authorities in their fields, have contributed their latest research papers to this volume. The topics include extension and applications of the regularity lemma, the existence of k-term arithmetic progressions in various subsets of the integers, extremal problems in hypergraphs theory, and random graphs, all of them beautiful, Szemerédi type mathematics. It also contains published accounts of the first two, very original and highly successful Polymath projects, one led by Tim Gowers and the other by Terry Tao.