Download or read book Hypergraphs and Designs written by Mario Gionfriddo and published by Nova Science Publishers. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hypergraphs written by C. Berge and published by Elsevier. This book was released on 1984-05-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hypergraph Theory written by Alain Bretto and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Coloring Mixed Hypergraphs Theory Algorithms and Applications written by Vitaly Ivanovich Voloshin and published by American Mathematical Soc.. This book was released on 2002 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hyper graph Designs written by George Michael Foust and published by . This book was released on 1998 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fuzzy Graphs and Fuzzy Hypergraphs written by John N. Mordeson and published by Physica. This book was released on 2012-11-08 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. Two very important and useful concepts are those of granularity and of nonlinear ap proximations. The concept of granularity has evolved as a cornerstone of Lotfi A.Zadeh's theory of perception, while the concept of nonlinear approx imation is the driving force behind the success of the consumer electronics products manufacturing. It is fair to say fuzzy graph theory paved the way for engineers to build many rule-based expert systems. In the open literature, there are many papers written on the subject of fuzzy graph theory. However, there are relatively books available on the very same topic. Professors' Mordeson and Nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs. In particular, the discussion on hypergraphs certainly is an innovative idea. For an experienced engineer who has spent a great deal of time in the lab oratory, it is usually a good idea to revisit the theory. Professors Mordeson and Nair have created such a volume which enables engineers and design ers to benefit from referencing in one place. In addition, this volume is a testament to the numerous contributions Professor John N. Mordeson and his associates have made to the mathematical studies in so many different topics of fuzzy mathematics.
Download or read book The Existence of Designs Via Iterative Absorption Hypergraph F designs for Arbitrary F written by Stefan Glock and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Existence of Designs via Iterative Absorption Hypergraph F Designs for Arbitrary F written by Stefan Glock and published by American Mathematical Society. This book was released on 2023-04-07 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Combinatorics written by Béla Bollobás and published by Cambridge University Press. This book was released on 1986-07-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
Download or read book Hypergraph Seminar written by C. Berge and published by Springer. This book was released on 2006-11-15 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Grafy hipergrafy systemy blok w written by and published by . This book was released on 1977 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graphs and Hypergraphs written by Claude Berge and published by . This book was released on 1973 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eulerian Properties of Design Hypergraphs and Hypergraphs with Small Edge Cuts written by Andrew Wagner and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Disjoint Union free 3 uniform Hypergraphs written by Leah Howard and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial Designs and Hypergraphs of Diameter One written by J. C.. Bermond and published by . This book was released on 1986 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graphs and Hypergraphs written by Claude Berge and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Graph and Hypergraph Theory written by Vitaly Ivanovich Voloshin and published by . This book was released on 2009 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalisation of Part I. The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring. The second part considers generalisations of Part I and discusses hypertrees, bipartite hypergraphs, hypercycles, chordal hypergraphs, planar hypergraphs and hypergraph colouring. There is an interaction between the parts and within the parts to show how ideas of generalisations work. The main point is to exhibit the ways of generalisations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hypergraphs. This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hypergraphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view.