Balanced tournament designs and related topics

A balanced tournament design of order n, BTD(n), is an n x (2n – 1) array defined on a set of 2n elements V such that (1) each cell of the array contains a pair of distinct elements from V, (2) every pair of distinct elements from V is contained in some cell, (3) each element is contained in each column, and (4) no element is contained in more than 2 cells of each row. BTD(n)s are very useful for scheduling certain types of round robin tournaments such as tennis and curling. Their existence has been completely settled. In this paper we survey the known results and discuss various extensions and generalizations.

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