Matroid Theory
Series: Oxford Graduate Texts in Mathematics;
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46 341 Ft
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Product details:
- Publisher Oxford University Press
- Date of Publication 17 December 1992
- ISBN 9780198535638
- Binding Hardback
- No. of pages544 pages
- Size 241x163x34 mm
- Weight 937 g
- Language English
- Illustrations numerous line drawings 0
Categories
Short 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 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 five hundred exercises and includes, for the first time in one place, short proofs of major theorems in the subject. The final chapter lists sixty unsolved problems and describes progress towards their solutions.
Long description:
What is the essence of the similarity between forests in a graph and linearly independent sets of columns in a matrix? Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph? Is it possible to test in polynomial time whether a matrix is totally unimodular? These questions form the basis of Matroid theory.
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 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 five hundred exercises and includes, for the first time in one place, short proofs of all but one of the major theorems in the subject. The final chapter lists sixty unsolved problems and describes progress towards their solutions.
Table of Contents:
Preliminaries
Basic definitions and examples
Duality
Minors
Connectivity
Graphic matroids
Representable matroids
Constructions
Higher connectivity
Binary matroids
Ternary matroids
The Splitter theorem
Submodular functions and matroid union
Regular matroids
Unsolved problems
References
Appendix. Some interesting matroids
Notation
Index
