Breaks, cuts, and patterns

We generalize the concept of a break by considering pairs of arbitrary rounds. We show that a set of home-away patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P=NPP=NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.

► The concept of a break is generalized by considering pairs of arbitrary rounds.
► Finding a set of home-away patterns minimizing the number of breaks is NP-hard.
► In case of identical break sets, the decision version becomes easy.