Complete Mixed Doubles Round Robin Tournaments

David R.Berman1, Ian N.Wakeling2
1Department of Computer Science University of North Carolina Wilmington Wilmington, NC 28403
2Qi Statistics Ltd. Penhales House, Ruscombe Berkshire RG10 9JN, UK ianQqistatistics.co.uk

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