Synopses & Reviews
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.
Synopsis
The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.
Synopsis
Text by a noted expert describes standard examples and investigation results, using elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. Includes numerous exercises. 1976 edition.
Table of Contents
PrefacePreliminaries1. Fundamental Concepts and Examples2. Duality3. Lattice Theory and Matroids4. Submatroids5. Matroid Connection6. Matroids, Graphs and Planarity7. Transversal Theory8. Covering and Packing 9. The Vector representation of Matroids10. Binary Matroids11. Matroids from Fields and Groups12. Block Designs and matroids13. Menger's Theorem and Linkings in Graphs14. Transversal Matroids and Related Topics15. Polynomials, Colouring Problems, Codes and packings16. Extremal Problems17. Maps between Matroids and Geometric Lattices18. Convex Polytopes associated with Matroids19. Combinatorial OPtimisation20. Infinite StructuresBibliographyIndex of SymbolsIndex