Complete Mixed Doubles Round Robin Tournaments

摘要

We present a new type of tournament design that we call a complete mixed doubles round robin tournament, CMDRR(n, A;), that generalizes spouse-avoiding mixed doubles round robin tournaments and strict Mitchell mixed doubles round robin tournaments. We show that 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 CMDRR(2n, 0) exists for all n ≥ 5 and a fully resolvable CMDRR(3n, n) exists for all n ≥ 5 and n odd. We prove a product theorem for constructing CMDRR(n, k).