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9780486796833

Topics on Tournaments in Graph Theory

by
  • ISBN13:

    9780486796833

  • ISBN10:

    0486796833

  • Format: Paperback
  • Copyright: 2015-06-17
  • Publisher: Dover Publications

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Summary

Tournaments, in this context, are directed graphs ― an important and interesting topic in graph theory. This concise volume collects a substantial amount of information on tournaments from throughout the mathematical literature. Suitable for advanced undergraduate students of mathematics, the straightforward treatment requires a basic familiarity with finite mathematics.
The fundamental definitions and results appear in the earlier sections, and most of the later sections can be read independently of each other. Subjects include irreducible and strong tournaments, cycles and strong subtournaments of a tournament, the distribution of 3-cycles in a tournament, transitive tournaments, sets of consistent arcs in a tournament, the diameter of a tournament, and the powers of tournament matrices. Additional topics include scheduling a tournament and ranking the participants, universal tournaments, the use of oriented graphs and score vectors, and many other subjects.

Author Biography

John W. Moon is Professor Emeritus of the University of Alberta.

Table of Contents

1. Introduction
2. Irreducible Tournaments
3. Strong Tournaments
4. Cycles in a Tournament
5. Strong Subtournaments of a Tournament
6. The Distribution of 3-cycles in aTournament
7. Transistive Tournaments
8. Sets of Consistent Arcs in a Tournament
9. The Parity of the Number of Spanning Paths of a Tournament
10. The Maximum Number of Spanning Paths of a Tournament
11. An Extremal Problem
12. The Diameter of a Tournament
13. The Powers of Tournament Matrices
14. Scheduling a Tournament
15. Ranking the Participants in a Tournament
16. The Minimum Number of Comparisons Necessary to Determine a Transitive Tournament
17. Universal Tournaments
18. Expressing Oriented Graphs as the Union of Bilevel Graphs
19. Oriented Graphs Induced by Voting Patterns
20. Oriented Graphs Induced by Team Comparisons
21. Criteria for a Score Vector
22. Score Vectors of Generalizations of Tournaments
23. The Number of Score Vectors
24. The Largest Score in a Tournament
25. A Reversal Theorem
26. Tournaments with a Given Automorphism Group
27. The Group of the Composition of Two Tournaments
28. The Maximum Order of the Group of a Tournament
29. The Number of Nonisomorphic Tournaments
Appendix
References
Index
    Author
    Subject    

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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