Matroid Theory

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.

• 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