Victor Bryant “Independence theory in combinatorics: An introductory account with applications to graphs and transversals”
Chapman and Hall | 1980 | ISBN: 0412162202 | 144 pages | Djvu | 2,6 Mb

Contents

1 Preliminaries
General introductory & historical remarks | Sets, families & graphs | Vector spaces; linear & affine independence | Exercises

2 Independence spaces
Axioms & some basic theorems | Some induced structures | Submodular functions | Sums of independence structures | Exercises

3 Graphic spaces
The cycle & cutset structures of a graph | Connections with vector spaces | Applications of independence theory to graphs | Exercises

4 Transversal spaces
Hall’s theorem & its generalization | The partial transversals of a family of sets | Duals of transversal structures | Extensions of Hall’s theorem | Applications | Exercises

5 Appendix on representability
Representability in general | Linear representability | Induced structures | Linear representability over specified fields | Some spaces which are not linearly representable | Exercises

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