Constructing fair single round robin tournaments regarding strength groups with a minimum number of breaks

In this paper, we present a constructive method to show the existence of group-balanced single round robin tournaments (SRRTs) with a minimum number of breaks, if the number of groups is a power of 2 with identical even group sizes. When the number of teams is a multiple of 4, we show the existence of group-changing SRRTs with a minimum number of breaks, if the union of some groups contains exactly half of the teams.