Matroid Theory

Author: J. G. Oxley

Publisher: Oxford University Press, USA

ISBN: 9780199202508

Category: Mathematics

Page: 532

View: 4447

The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics. This new in paperback version of the classic "Matroid Theory" by James Oxley provides a comprehensive introduction to matroid theory, covering the very basics to more advanced topics. With over 500 exercisesand proofs of major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science. The final chapter lists sixty unsolved problems and describes progress towards their solutions.

Matroid Theory

Author: D. J. A. Welsh

Publisher: Courier Corporation

ISBN: 0486474399

Category: Mathematics

Page: 433

View: 7905

The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.

Matroid Theory

AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory, July 2-6, 1995, University of Washington, Seattle

Author: Joseph Edmond Bonin

Publisher: American Mathematical Soc.

ISBN: 0821805088

Category: Mathematics

Page: 418

View: 854

This volume contains the proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory held at the University of Washington, Seattle. The book features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour. Walter Whiteley's article unifies applications of matroid theory to constrained geometrical systems, including the rigidity of bar-and-joint frameworks, parallel drawings, and splines. These widely accessible articles contain many new results and directions for further research and applications. The surveys are complemented by selected short research papers. The volume concludes with a chapter of open problems. Features self-contained, accessible surveys of three active research areas in matroid theory; many new results; pointers to new research topics; a chapter of open problems; mathematical applications; and applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.

Matroid theory

Author: László Lovász,András Recski

Publisher: N.A

ISBN: N.A

Category: Science

Page: 438

View: 4032


Matroids: A Geometric Introduction

Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 1139536087

Category: Mathematics

Page: N.A

View: 3219

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

A Source Book in Matroid Theory

Author: KUNG

Publisher: Springer Science & Business Media

ISBN: 1468491997

Category: Mathematics

Page: 413

View: 7980

by Gian-Carlo Rota The subjects of mathematics, like the subjects of mankind, have finite lifespans, which the historian will record as he freezes history at one instant of time. There are the old subjects, loaded with distinctions and honors. As their problems are solved away and the applications reaped by engineers and other moneymen, ponderous treatises gather dust in library basements, awaiting the day when a generation as yet unborn will rediscover the lost paradise in awe. Then there are the middle-aged subjects. You can tell which they are by roaming the halls of Ivy League universities or the Institute for Advanced Studies. Their high priests haughtily refuse fabulous offers from eager provin cial universities while receiving special permission from the President of France to lecture in English at the College de France. Little do they know that the load of technicalities is already critical, about to crack and submerge their theorems in the dust of oblivion that once enveloped the dinosaurs. Finally, there are the young subjects-combinatorics, for instance. Wild eyed individuals gingerly pick from a mountain of intractable problems, chil dishly babbling the first words of what will soon be a new language. Child hood will end with the first Seminaire Bourbaki. It could be impossible to find a more fitting example than matroid theory of a subject now in its infancy. The telltale signs, for an unfailing diagnosis, are the abundance of deep theorems, going together with a paucity of theories.

Theory of Matroids

Author: Neil White

Publisher: Cambridge University Press

ISBN: 0521309379

Category: Mathematics

Page: 316

View: 4139

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

Topics in Matroid Theory

Author: Leonidas S. Pitsoulis

Publisher: Springer Science & Business Media

ISBN: 1461489571

Category: Mathematics

Page: 127

View: 4780

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

A Lost Mathematician, Takeo Nakasawa

The Forgotten Father of Matroid Theory

Author: Hirokazu Nishimura,Susumu Kuroda

Publisher: Springer Science & Business Media

ISBN: 9783764385736

Category: Mathematics

Page: 236

View: 4242

Matroid theory was invented in the middle of the 1930s by two mathematicians independently, namely, Hassler Whitney in the USA and Takeo Nakasawa in Japan. Whitney became famous, but Nakasawa remained anonymous until two decades ago. He left only four papers to the mathematical community, all of them written in the middle of the 1930s. It was a bad time to have lived in a country that had become as eccentric as possible. Just as Nazism became more and more flamboyant in Europe in the 1930s, Japan became more and more esoteric and fanatical in the same time period. This book explains the little that is known about Nakasawa’s personal life in a Japan that had, among other failures, lost control over its military. This book contains his four papers in German and their English translations as well as some extended commentary on the history of Japan during those years. The book also contains 14 photos of him or his family. Although the veil of mystery surrounding Nakasawa’s life has only been partially lifted, the work presented in this book speaks eloquently of a tragic loss to the mathematical community.

Matroid Theory and Its Applications

Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), Italy, August 24 - September 2, 1980

Author: A. Barlotti

Publisher: Springer Science & Business Media

ISBN: 9783642111105

Category: Mathematics

Page: 424

View: 6565

Lectures: T.H. Brylawski: The Tutte polynomial.- D.J.A. Welsh: Matroids and combinatorial optimisation.- Seminars: M. Barnabei, A. Brini, G.-C. Rota: Un’introduzione alla teoria delle funzioni di Möbius.- A. Brini: Some remarks on the critical problem.- J. Oxley: On 3-connected matroids and graphs.- R. Peele: The poset of subpartitions and Cayley’s formula for the complexity of a complete graph.- A. Recski: Engineering applications of matroids.- T. Zaslavisky: Voltage-graphic matroids.

Matrices and Matroids for Systems Analysis

Author: Kazuo Murota

Publisher: Springer Science & Business Media

ISBN: 3642039944

Category: Mathematics

Page: 483

View: 305

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 543

This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

Combinatorial Optimization

Networks and Matroids

Author: Eugene Lawler

Publisher: Courier Corporation

ISBN: 048614366X

Category: Mathematics

Page: 400

View: 1199

Perceptive text examines shortest paths, network flows, bipartite and nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. Suitable for courses in combinatorial computing and concrete computational complexity.

Combinatorial Rigidity

Author: Jack E. Graver,Brigitte Servatius,Herman Servatius

Publisher: American Mathematical Soc.

ISBN: 0821838016

Category: Mathematics

Page: 172

View: 2439

This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. The book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibiolography with over 150 entries. The book is aimed at graduate students and researchers in graph theory and combinatorics or in fields which apply the structural aspects of these subjects in architecture and engineering. Accessible to those who have had an introduction to graph theory at the senior or graduate level, the book would be suitable for a graduate course in graph theory.

Oriented Matroids

Author: Anders Björner

Publisher: Cambridge University Press

ISBN: 9780521777506

Category: Mathematics

Page: 548

View: 5476

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Matroid Decomposition

Author: K. Truemper

Publisher: Leibniz Company

ISBN: 1483276627

Category: Mathematics

Page: 408

View: 1891

Matroid Decomposition deals with decomposition and composition of matroids. The emphasis is on binary matroids, which are produced by the matrices over the binary field GF(2). Different classes of matroids are described (graphic, regular, almost regular, max-flow min-cut), along with polynomial testing algorithms. Representative applications and, except for the almost-regular case, characterizations in terms of excluded minors are given. In addition, excluded minor characterizations of both binary and ternary matroids are presented. Comprised of 13 chapters, this book begins with an introduction to basic definitions concerning graphs and matrices, followed by a discussion on binary matroids. Subsequent chapters focus on some elementary constructions of graphs and binary matroids; a simple yet effective method called the path shortening technique for establishing basic connectivity relationships and certain results about the intersection and partitioning of matroids; an algorithm for identifying certain matroid separations; and the so-called splitter theorem. Fundamental notions and theorems about matroid decomposition and composition are described, along with a very important property of real matrices called total unimodularity. The book concludes with an analysis of flows in matroids based on ideas from flows in graphs. This monograph will be of interest to students and practitioners in diverse fields such as civil, electrical, and mechanical engineering, as well as computer science and mathematics.