Constructing fair round robin tournaments with a minimum number of breaks

Given nn clubs with two teams each, we show that, if nn is even, it is possible to construct a schedule for a single round robin tournament satisfying the following properties: the number of breaks is 2n−22n−2, teams of the same club never play at home simultaneously, and they play against each other in the first round. We also consider a fairness constraint related to different playing strengths of teams competing in the tournament.