Mathematics Independence theory in combinatorics: An introductory account with applications to graphs and transversals (0412162202)

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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

Hints & solutions to the exercises

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	Study Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications Martin Charles Golumbic, Irith Ben-Arroyo Hartman, "Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications"Springer \| ISBN 038724347X \| Year 2005 \| 301 pages \| PDF \| 3.7 MBGraph Theory, Combinatorics and Algorithms: Inte ...
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	Study Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications Martin Charles Golumbic, Irith Ben-Arroyo Hartman, "Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications"Springer \| ISBN 038724347X \| Year 2005 \| 301 pages \| PDF \| 3.7 MBGraph Theory, Combinatorics and Algorithms: Inte ...
	Science/Engineering Theory and Application of Graphs (Network Theory and Applications) Junming Xu, "Theory and Application of Graphs (Network Theory and Applications)"Publisher: Springer \| Pages: 344 \| ISBN: 1402075405 \| PDF \| 8.76 MBThis book considers a graph as a mathematical structure on a set of elements with a binary re ...
	Science/Engineering Combinatorics: With Emphasis on the Theory of Graphs Jack E. Graver, "Combinatorics: With Emphasis on the Theory of Graphs" Springer \| 1977 \| ISBN: 0387902457 \| 351 pages \| Djvu \| 4,6 MB An undergraduate course in linear algebra is prerequisite to the com- prehension of most of this book. B ...
	Graphs Theory and Applications ean-Claude Fournier, "Graphs Theory and Applications" Wiley-ISTE \| 2009 \| ISBN: 1848210701 \| 282 pages \| PDF \| 1,3 MB This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all ...
	Mathematics Graphs and order: the role of graphs in the theory of ordered sets and its applications TitleGraphs and order: the role of graphs in the theory of ordered sets and its applicationsIssue 147 of NATO ASI series, NATOVolume 147 of NATO ASI series. Series C, Mathematical and physical sciences ; no.147Volume 147 of NATO Science Ser ...
	Graphs and Applications: An Introductory Approach Graphs and Applications: An Introductory ApproachGraphs and Applications: An Introductory ApproachPublisher: Springer \| pages: 444 \| 2000 \| ISBN: 185233259X \| PDF \| 24 mbDiscrete Mathematics is one of the fastest growing areas in ma ...

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