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基本説明
New in paperback. Hardcover was published in 1992. Matroid theory is a branch of discrete mathematics with close toes to graph theory, projective geometry, and operations research. This book begins with a comprehensive introduction to the subject suitable for use in a one-semester graduate course.
Full Description
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.
Contents
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
