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One-Factorizations

  • Book
  • © 1997

Overview

Authors:
  1. W. D. Wallis

    1. Southern Illinois University, Carbondale, USA

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Part of the book series: Mathematics and Its Applications (MAIA, volume 390)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Graphs

    • W. D. Wallis
    Pages 1-6

  3. Walks, Paths and Cycles

    • W. D. Wallis
    Pages 7-11

  4. One-Factors and One-Factorizations

    • W. D. Wallis
    Pages 13-24

  5. Orthogonal One-Factorizations

    • W. D. Wallis
    Pages 25-31

  6. Tournament Applications of One-Factorizations

    • W. D. Wallis
    Pages 33-42

  7. A General Existence Theorem

    • W. D. Wallis
    Pages 43-49

  8. Graphs without One-Factors

    • W. D. Wallis
    Pages 51-56

  9. Edge-Colorings

    • W. D. Wallis
    Pages 57-66

  10. One-Factorizations and Triple Systems

    • W. D. Wallis
    Pages 67-73

  11. Starters

    • W. D. Wallis
    Pages 75-83

  12. Invariants of One-Factorizations

    • W. D. Wallis
    Pages 85-95

  13. Automorphisms and Asymptotic Numbers of One-Factorizations

    • W. D. Wallis
    Pages 97-106

  14. Systems of Distinct Representatives

    • W. D. Wallis
    Pages 107-110

  15. Subfactorizations and Asymptotic Numbers of One-Factorizations

    • W. D. Wallis
    Pages 111-118

  16. Cyclic One-Factorizations

    • W. D. Wallis
    Pages 119-124

  17. Perfect Factorizations

    • W. D. Wallis
    Pages 125-130

  18. One-Factorizations of Multigraphs

    • W. D. Wallis
    Pages 131-140

  19. Maximal Sets of Factors

    • W. D. Wallis
    Pages 141-152

  20. The One-Factorization Conjecture

    • W. D. Wallis
    Pages 153-164
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About this book

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.

Authors and Affiliations

  • Southern Illinois University, Carbondale, USA

    W. D. Wallis

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