Matroid theory
著者
書誌事項
Matroid theory
（Oxford graduate texts in mathematics, 3）
Oxford University Press, 2006
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注記
Originally published: 1992
Includes bibliographical references and index
内容説明・目次
内容説明
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 exercises and 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.
目次
- Preface
- Preliminaries
- 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. Ternary matroids
- 11. The Splitter theorem
- 12. Submodular functions and matroid union
- 13. Regular matroids
- 14. Unsolved problems
- References
- Appendix. Some interesting matroids
- Notation
- Index
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