Matroid Theory

Matroid Theory

by D. J. A. Welsh

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Overview

The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. Aimed at advanced undergraduate and graduate students, this text is one of the earliest substantial works on matroid theory. Its author, D. J. A. Welsh, Professor of Mathematics at Oxford University, has exercised a profound influence over the theory's development.
The first half of the text describes standard examples and investigation results, using elementary proofs to develop basic matroid properties and referring readers to the literature for more complex proofs. The second half advances to a more sophisticated treatment, addressing a variety of research topics. Praised by the Bulletin of the American Mathematical Society as "a useful resource for both the novice and the expert," this text features numerous helpful exercises.

Product Details

ISBN-13: 9780486474397
Publisher: Dover Publications
Publication date: 06/17/2010
Series: Dover Books on Mathematics Series
Pages: 448
Product dimensions: 5.30(w) x 8.40(h) x 0.60(d)

Table of Contents

Preface
Preliminaries
1. Fundamental Concepts and Examples
2. Duality
3. Lattice Theory and Matroids
4. Submatroids
5. Matroid Connection
6. Matroids, Graphs and Planarity
7. Transversal Theory
8. Covering and Packing
9. The Vector representation of Matroids
10. Binary Matroids
11. Matroids from Fields and Groups
12. Block Designs and matroids
13. Menger's Theorem and Linkings in Graphs
14. Transversal Matroids and Related Topics
15. Polynomials, Colouring Problems, Codes and packings
16. Extremal Problems
17. Maps between Matroids and Geometric Lattices
18. Convex Polytopes associated with Matroids
19. Combinatorial OPtimisation
20. Infinite Structures
Bibliography
Index of Symbols
Index

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