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
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.
`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
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