Corr. ed. (Project Gutenberg, 2013) — New York: Holt, Rinehart and Winston, 1968. — 142 p.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. Dover (2015) republication of Topics on Tournaments, originally published by Holt, Rinehart & Winston, Inc., New York, 1968.Introduction. Irreducible Tournaments. Strong Tournaments. Cycles in a Tournament. Strong Subtournaments of a Tournament. The Distribution of 3-cycles in a Tournament. Transitive Tournaments. Sets of Consistent Arcs in a Tournament. The Parity of the Number of Spanning Paths of a Tournament. The Maximum Number of Spanning Paths of a Tournament. An Extremal Problem. The Diameter of a Tournament. The Powers of Tournament Matrices. Scheduling a Tournament. Ranking the Participants in a Tournament. The Minimum Number of Comparisons Necessary to Determine a Transitive Tournament. Universal Tournaments. Expressing Oriented Graphs as the Union of Bilevel Graphs. Oriented Graphs Induced by Voting Patterns. Oriented Graphs Induced by Team Comparisons. Criteria for a Score Vector. Score Vectors of Generalizations of Tournaments. The Number of Score Vectors. The Largest Score in a Tournament. A Reversal Theorem. Tournaments with a Given Automorphism Group. The Group of the Composition of Two Tournaments . The Maximum Order of the Group of a Tournament. The Number of Nonisomorphic Tournaments. Appendix. References.True PDF (HQ)
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