Topics on Tournaments in Graph Theory

Download or read book Topics on Tournaments in Graph Theory written by John W. Moon and published by Courier Dover Publications. This book was released on 2015-05-05 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.