Topics on Tournaments

In the world of graphs, few structures are as deceptively simple yet endlessly rich as the tournament: a complete directed graph where every pair of vertices is joined by a single one-way edge. Moon's definitive text unveils the deep combinatorial properties of these objects, from Landau's theorems on score sequences to the intricate paths that traverse every vertex exactly once. The mathematics here balances accessibility with genuine depth, making it equally suitable for a beginning graduate student encountering tournament theory for the first time and a researcher seeking a coherent catalogue of classical results. Each chapter builds carefully from foundations to frontier, illuminating how apparently trivial constraints the direction of every possible matchup can generate profound questions about structure, connectivity, and order. The subject finds applications across economics, voting theory, and biology, yet the book remains firmly focused on the pure beauty of the combinatorial landscape. This is a book for anyone who has ever looked at a simple competition bracket and wondered what mathematical secrets it contained.