Grok a Book

Topics on Tournaments

John W. Moon

About the book

Tournaments are complete directed graphs, and derive their name from how they naturally model outcomes of round-robin tournaments. The study of tournaments is a rich area of graph theory, with applications to sports, voting, and ranking. This was an exploration of the combinatorial aspects of tournaments.

Prerequisites

The equivalent of a first course in discrete math at an undergraduate level would be useful background. Some familiarity with graphs in general is desirable but not required.

Sessions

22 of 28 sessions were recorded. Dates are IST.

  1. 5 May Introduction Basic definitions and fundamental concepts of tournaments ▶ 1 h 08 min notes
  2. 6 May Irreducible Tournaments Exploring irreducible tournaments and their properties ▶ 58 min
  3. 7 May Strong Tournaments Understanding strong tournaments and their characteristics ▶ 33 min
  4. 8 May Cycles in a Tournament Analysis of cycles and their significance in tournaments ▶ 37 min
  5. 11 May Transitive Tournaments Exploring transitive tournaments and their unique properties ▶ 41 min
  6. 12 May Sets of Consistent Arcs in a Tournament Understanding consistent arc sets and their implications ▶ 1 h 00 min
  7. 13 May The Parity of the Number of Spanning Paths of a Tournament Examining parity properties of spanning paths ▶ 1 h 15 min
  8. 15 May An Extremal Problem Exploring extremal problems in tournament theory ▶ 1 h 09 min
  9. 16 May The Diameter of a Tournament Understanding tournament diameter and its implications ▶ 42 min
  10. 18 May Scheduling a Tournament Practical applications in tournament scheduling ▶ 1 h 25 min
  11. 19 May Ranking the Participants in a Tournament Methods and algorithms for ranking tournament participants ▶ 1 h 03 min
  12. 21 May Universal Tournaments Exploring the concept and properties of universal tournaments ▶ 1 h 02 min
  13. 22 May Expressing Oriented Graphs as the Union of Bilevel Graphs Representation theory for oriented graphs in tournaments ▶ 1 h 02 min
  14. 23 May Oriented Graphs Induced by Voting Patterns Applications of tournament theory to voting systems ▶ 46 min
  15. 24 May Oriented Graphs Induced by Team Comparisons Applications of tournament theory to sports and competitions ▶ 59 min
  16. 26 May Score Vectors of Generalizations of Tournaments Extending score vector concepts to generalized tournaments ▶ 56 min
  17. 27 May The Number of Score Vectors Combinatorial analysis of possible score vectors ▶ 1 h 05 min
  18. 28 May The Largest Score in a Tournament Extremal analysis of maximum scores in tournaments ▶ 1 h 32 min
  19. 29 May A Reversal Theorem Exploring reversal properties in tournament theory ▶ 1 h 01 min
  20. 30 May Tournaments with a Given Automorphism Group Algebraic analysis of tournament symmetries ▶ 52 min
  21. 31 May The Group of the Composition of Two Tournaments Understanding compositional properties of tournament groups ▶ 58 min
  22. 1 Jun The Maximum Order of the Group of a Tournament Exploring maximum order properties in tournament groups ▶ 42 min