Complete Mixed Doubles Round Robin Tournaments

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 \( n \geq 5 \) and a fully resolvable \( \text{CMDRR}(3n, n) \) exists for all \( n \geq 5 \) and \( n \) odd. We prove a product theorem for constructing \( \text{CMDRR}(n, k) \).