The Existence of Interval-Balanced Tournament Designs

Abstract

A tournament design, $TD(n,c)$, is a $c$-row array of the $(\genfrac{}{}{0ex}{}{n}{2})$ pairs of elements from an $n$-set such that every element appears at most once in each column and there are no empty cells. An interval balanced tournament design, $\text{IBTD}(n,c)$, satisfies the added condition that the appearances of each element are equitably distributed amongst the columns of the design. We settle the existence question for all $\text{IBTD}(n,c)$s by showing that they can be constructed for all admissible parameters and discuss the application of $\text{IBTD}$s to scheduling round robin tournaments fairly with respect to the amount of rest allocated to each participant.