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.