Matroid Theory

Paperback | March 17, 2011

byJames Oxley

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* 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 theirapplications 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 thesubject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.

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* 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 li...

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 ...

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Format:PaperbackDimensions:704 pages, 9.21 × 6.14 × 0.01 inPublished:March 17, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199603391

ISBN - 13:9780199603398

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Table of Contents

1. Basic definitions and examples2. Duality3. Minors4. Connectivity5. Graphic matroids6. Representable matroids7. Constructions8. Higher connectivity9. Binary matroids10. Excluded-minor theorems11. Submodular functions and matroid union12. The Splitter Theorem13. Seymour's Decomposition Theorem14. Research in representability and structure15. Unsolved problemsSome interesting matroidsReferencesNotationIndex

Editorial Reviews

"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