Table of Contents
1 Introduction 1
2 Irreducible Tournaments 2
3 Strong Tournaments 4
4 Cycles in a Tournament 5
5 Strong Subtournaments of a Tournament 8
6 The Distribution of 3-cycles in a Tournament 11
7 Transitive Tournaments 14
8 Sets of Consistent Arcs in a Tournament 19
9 The Parity of the Number of Spanning Paths of a Tournament 21
10 The Maximum Number of Spanning Paths of a Tournament 26
11 An Extremal Problem 28
12 The Diameter of a Tournament 32
13 The Powers of Tournament Matrices 34
14 Scheduling a Tournament 39
15 Ranking the Participants in a Tournament 42
16 The Minimum Number of Comparisons Necessary to Determine a Transitive Tournament 47
17 Universal Tournaments 49
18 Expressing Oriented Graphs as the Union of Bilevel Graphs 51
19 Oriented Graphs Induced by Voting Patterns 56
20 Oriented Graphs Induced by Team Comparisons 57
21 Criteria for a Score Vector 61
22 Score Vectors of Generalizations of Tournaments 63
23 The Number of Score Vectors 65
24 The Largest Score in a Tournament 71
25 A Reversal Theorem 73
26 Tournaments with a Given Automorphism Group 74
27 The Group of the Composition of Two Tournaments 78
28 The Maximum Order of the Group of a Tournament 81
29 The Number of Nonisomorphic Tournaments 84
Appendix 91
References 96
Index
Author 102
Subject 104
