Scheduling partial round robin tournaments subject to home away pattern sets
In this paper a sports league scheduling problem is studied from a theoretical point of view. The objective is to find a round robin tournament schedule for \(2n\) teams and \(2n-1\) rounds where each team plays against each other team exactly once and every team plays one match per round. Additionally, a given home-away pattern set has to be respected which determines for every team and every round whether the team has to play home or away in that round. For the question whether a feasible schedule exists which is compatible with the given HAP set necessary conditions were proposed by \textit{D. Briskorn} [Oper. Res. Lett. 36, No. 3, 283--284 (2008; Zbl 1142.91364)], who conjectured that they are also sufficient. In this paper this conjecture is rewritten in terms of perfect matchings. By studying the Hilbert basis of a monoid in the affine space generated by perfect matchings the problem is generalized to situations where not all teams play against each other. It is shown that for this more general situation the conjecture is false, but holds for specially structured graphs.
scientific article; zbMATH DE number 5576436