One-Factorizations
(Sprache: Englisch)
This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook...
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This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook at the graduate level and also as a professional reference. The topic of one-factorizations fits into the theory of combinatorial designs just as much as it does into graph theory. Factors and factorizations occur as building blocks in the theory of designs in a number of places. Our approach owes as much to design theory as it does to graph theory. It is expected that nearly all readers will have some background in the theory of graphs, such as an advanced undergraduate course in Graph Theory or Applied Graph Theory. However, the book is self-contained, and the first two chapters are a thumbnail sketch of basic graph theory. Many readers will merely skim these chapters, observing our notational conventions along the way. (These introductory chapters could, in fact, enable some instructors to Ilse the book for a somewhat eccentric introduction to graph theory.) Chapter 3 introduces one-factors and one-factorizations. The next two chapters outline two major application areas: combinatorial arrays and tournaments. These two related areas have provided the impetus for a good deal of study of one-factorizations.
This is a specialized textbook on graph factorizations, an area which lies partly in graph theory and partly in the theory of combinational designs. It is the first full-size book on its particular subject, which has previously been treated only in survey papers and in chapters in books on design theory and on graph decompositions and matching theory. The book is intended for beginning graduate students in Combinatorial Mathematics, and may be used as a text for a special topics course; but it reaches to the boundaries of current research and will also prove useful as a reference source for professionals in the field. It contains a number of easy exercises, together with some which are challenging, and a few unsolved problems. There is an extensive bibliography.
Inhaltsverzeichnis zu „One-Factorizations “
List of Figures. List of Tables. Preface1. Graphs
2. Walks, Paths and Cycles
3. One-Factors and One-Factorizations
4. Orthogonal One-Factorizations
5. Tournament Applications of One-Factorizations
6. A General Existence Theorem
7. Graphs without One-Factors
8. Edge-Colorings
9. One-Factorizations and Triple Systems
10. Starters
11. Invariants of One-Factorizations
12. Automorphisms and Asymptotic Numbers of One-Factorizations
13. Systems of Distinct Representatives
14. Subfactorizations and Asymptotic Numbers of One-Factorizations
15. Cyclic One-Factorizations
16. Perfect Factorizations
17. One-Factorizations of Multigraphs
18. Maximal Sets of Factors
19. The One-Factorization Conjecture
20. Premature Sets of Factors
21. Cartesian Products
22. Kotzig's Problem
23. Other Products. A. One-Factorizations of K10. B. Generators of Simple Indecomposable Factorizations. C. Generators of Nonsimple Indecomposable Factorizations. References. Index
Bibliographische Angaben
- Autor: W. D. Wallis
- 2010, Softcover reprint of hardcover 1st ed. 1997, XIV, 242 Seiten, Maße: 17 x 24,4 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441947663
- ISBN-13: 9781441947666
Sprache:
Englisch
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