Matroid Theory
2nd Edition
Published on 24. February 2011
Book
Paperback/Softback
704 pages
978-0-19-960339-8 (ISBN)
Description
* What is the essence of the similarity between linearly independent sets of columns of a matrix and forests in a graph?
* Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph?
* Can we test in polynomial time whether a matrix is totally unimodular?
Matroid theory examines and answers questions like these. Seventy-five years of study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering.
This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. The book contains over seven hundred exercises and includes, for the first time in one place, proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.
* Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph?
* Can we test in polynomial time whether a matrix is totally unimodular?
Matroid theory examines and answers questions like these. Seventy-five years of study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering.
This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. The book contains over seven hundred exercises and includes, for the first time in one place, proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.
Reviews / Votes
Review from previous edition It includes more background, such as finite fields and finite projective and affine geometries, and the level of the exercises is well suited to graduate students. The book is well written and includes a couple of nice touches ... this is a very useful book. I recommend it highly both as an introduction to matroid theory and as a reference work for those already seriously interested in the subject, whether for its own sake or for its applications to other fields. * AMS Bulletin * Whoever wants to know what is happening in one of the most exciting chapters of combinatorics has no choice but to buy and peruse Oxley's treatise. * The Bulletin of Mathematics * This book is an excellent graduate textbook and reference book on matroid theory. The care that went into the writing of this book is evident by the quality of the exposition. * Mathematical Reviews *More details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Mathematicians, computer scientists and engineers with interests in combinatorics and combinatorial optimization, graph theory, lattice theory or projective geometry.
Edition type
Revised edition
Illustrations
266 illustrations
Dimensions
Height: 232 mm
Width: 157 mm
Thickness: 40 mm
Weight
1044 gr
ISBN-13
978-0-19-960339-8 (9780199603398)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
James Oxley
Matroid Theory
Book
02/2011
2nd Edition
Oxford University Press
€243.70
Shipment within 15-20 days
Person
James Oxley was born in Australia. After completing his undergraduate studies there, he received his doctorate from Oxford University in 1978 under the supervision of Dominic Welsh. After a postdoctoral position at the Australian National University and a Fulbright Postdoctoral Fellowship at the University of North Carolina, he began working at Louisiana State University in 1982. He has been an Alumni Professor there since 1999. He has written more than one hundred research papers in matroid theory and graph theory and has given over fifty conference talks including plenary addresses at the British Combinatorial Conference in 2001 and an American Mathematical Society meeting in 2002. Fourteen students have completed doctorates under his supervision and he is currently advising five other doctoral candidates. In 1999, he was named LSU's Distinguished Research Master for Engineering, Science, and Technology. From April until July 2005, he was a Visiting Research Fellow at Merton College, Oxford.
Content
1. Basic definitions and examples ; 2. Duality ; 3. Minors ; 4. Connectivity ; 5. Graphic matroids ; 6. Representable matroids ; 7. Constructions ; 8. Higher connectivity ; 9. Binary matroids ; 10. Excluded-minor theorems ; 11. Submodular functions and matroid union ; 12. The Splitter Theorem ; 13. Seymour's Decomposition Theorem ; 14. Research in representability and structure ; 15. Unsolved problems ; Some interesting matroids ; References ; Notation ; Index