Complete Mixed Doubles Round Robin Tournaments

Abstract

We present a new type of tournament design that we call a complete mixed doubles round robin tournament, $\text{CMDRR}(n,k)$, that generalizes spouse-avoiding mixed doubles round robin tournaments and strict Mitchell mixed doubles round robin tournaments. We show that $\text{CMDRR}(n,k)$ exist for all allowed values of $n$ and $k$ apart from 4 exceptions and 31 possible exceptions. We show that a fully resolvable $\text{CMDRR}(2n,0)$ exists for all $n\ge 5$ and a fully resolvable $\text{CMDRR}(3n,n)$ exists for all $n\ge 5$ and $n$ odd. We prove a product theorem for constructing $\text{CMDRR}(n,k)$.