Imbalance in Tournament Designs
by
D. Fronček
Ostrava
Coauthors: F. Franek (Hamilton), A. Rosa (Hamilton)

We introduce two measures of imbalance, the team imbalance, and the field imbalance, in a tournament design. In a (round-robin) tournament of 2n teams, each team plays each other team exactly once. The n(2n-1) games are played in 2n-1 rounds, with n games in each round; each team sees action in each round. A schedule for a tournament is equivalent to a 1-factorization of the complete graph K_2n, i.e. to a partition of the edges of K_2n into 1-factors (i.e. perfect matchings). A tournament design is a tournament, together with an assignment of games to n given fields; in each round, exactly one game is assigned to a field. It is usually, but not always, desirable to strive for some sort of balance in assigning teams to play games at particular fields. It is the associated notion of imbalance (both team imbalance and field imbalance) that we attempt to take a closer look at in this article. We provide the necessary definitions and briefly survey the known results on balanced tournament designs. Then we provide some bounds for the imbalances as well as recursive constructions for homogeneous tournaments.

This research was supported by the NSERC of Canada Grant No. OGP0025112 (FF), No. GP007268 (AR), and by the GA of the Czech Republic Grant No. 201/98/1451 (DF).

Date received: May 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafd-08.