| Hardcover ISBN: | 978-0-8218-4759-6 |
| Product Code: | CHEL/367.H |
| List Price: | $79.00 |
| MAA Member Price: | $71.10 |
| AMS Member Price: | $71.10 |
| Electronic ISBN: | 978-1-4704-1575-4 |
| Product Code: | CHEL/367.H.E |
| List Price: | $79.00 |
| MAA Member Price: | $71.10 |
| AMS Member Price: | $63.20 |
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Book DetailsAMS Chelsea PublishingVolume: 367; 2009; 547 ppMSC: Primary 05; 90;
This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics. The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in 1986, by launching (among other things) the Markov Chain Monte Carlo method.
ReadershipGraduate students and research mathematicians interested in graph theory, combinatorics, combinatorial optimization, or graph algorithms.
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Table of Contents
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Chapters
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Chapter 1. Matchings in bipartite graphs
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Chapter 2. Flow theory
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Chapter 3. Size and structure of maximum matchings
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Chapter 4. Bipartite graphs with perfect matchings
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Chapter 5. General graphs with perfect matchings
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Chapter 6. Some graph-theoretical problems related to matchings
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Chapter 7. Matching and linear programming
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Chapter 8. Determinants and matchings
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Chapter 9. Matching algorithms
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Chapter 10. The $f$-factor problem
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Chapter 11. Matroid matching
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Chapter 12. Vertex packing and covering
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Appendix: Developments in matching theory since this book was first published
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Additional Material
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This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics. The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in 1986, by launching (among other things) the Markov Chain Monte Carlo method.
Graduate students and research mathematicians interested in graph theory, combinatorics, combinatorial optimization, or graph algorithms.
-
Chapters
-
Chapter 1. Matchings in bipartite graphs
-
Chapter 2. Flow theory
-
Chapter 3. Size and structure of maximum matchings
-
Chapter 4. Bipartite graphs with perfect matchings
-
Chapter 5. General graphs with perfect matchings
-
Chapter 6. Some graph-theoretical problems related to matchings
-
Chapter 7. Matching and linear programming
-
Chapter 8. Determinants and matchings
-
Chapter 9. Matching algorithms
-
Chapter 10. The $f$-factor problem
-
Chapter 11. Matroid matching
-
Chapter 12. Vertex packing and covering
-
Appendix: Developments in matching theory since this book was first published
