Topics on Tournaments in Graph Theory

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.

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

1. Introduction 2. Irreducible Tournaments3. Strong Tournaments4. Cycles in a Tournament5. Strong Subtournaments of a Tournament6. The Distribution of 3-cycles in aTournament7. Transistive Tournaments8. Sets of Consistent Arcs in a Tournament9. The Parity of the Number of Spanning Paths of a Tournament10. The Maximum Number of Spanning Paths of a Tournament11. An Extremal Problem12. The Diameter of a Tournament13. The Powers of Tournament Matrices14. Scheduling a Tournament15. Ranking the Participants in a Tournament16. The Minimum Number of Comparisons Necessary to Determine a Transitive Tournament17. Universal Tournaments18. Expressing Oriented Graphs as the Union of Bilevel Graphs19. Oriented Graphs Induced by Voting Patterns20. Oriented Graphs Induced by Team Comparisons21. Criteria for a Score Vector22. Score Vectors of Generalizations of Tournaments23. The Number of Score Vectors24. The Largest Score in a Tournament25. A Reversal Theorem26. Tournaments with a Given Automorphism Group27. The Group of the Composition of Two Tournaments28. The Maximum Order of the Group of a Tournament29. The Number of Nonisomorphic TournamentsAppendixReferencesIndex    Author    Subject