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One-Factorizations : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - W. D. Wallis

One-Factorizations

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

Published: 31st December 1996
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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.

List of Figures
List of Tables
Preface
Graphsp. 1
Walks, Paths and Cyclesp. 7
One-Factors and One-Factorizationsp. 13
Orthogonal One-Factorizationsp. 25
Tournament Applications of One-Factorizationsp. 33
A General Existence Theoremp. 43
Graphs without One-Factorsp. 51
Edge-Coloringsp. 57
One-Factorizations and Triple Systemsp. 67
Startersp. 75
Invariants of One-Factorizationsp. 85
Automorphisms and Asymptotic Numbers of One-Factorizationsp. 97
Systems of Distinct Representativesp. 107
Subfactorizations and Asymptotic Numbers of One-Factorizationsp. 111
Cyclic One-Factorizationsp. 119
Perfect Factorizationsp. 125
One-Factorizations of Multigraphsp. 131
Maximal Sets of Factorsp. 141
The One-Factorization Conjecturep. 153
Premature Sets of Factorsp. 165
Cartesian Productsp. 173
Kotzig's Problemp. 181
Other Productsp. 193
One-Factorizations of K[subscript 10]p. 201
Generators of Simple Indecomposable Factorizationsp. 215
Generators of Nonsimple Indecomposable Factorizationsp. 223
Referencesp. 225
Indexp. 239
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792343233
ISBN-10: 0792343239
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 242
Published: 31st December 1996
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.59