Using the applets contains general information.
A Glossary explains the used notions.
Under Literature references for the construction
methods can be found.
Single round robin tournaments
In a single round robin tournament each team plays against each other team exactly once. If the number of teams n is even, the schedules contain n-1 rounds and each team plays exactly one match in each round. If n is odd, the schedules contain n rounds and in each round one team has a bye (i.e. it does not play).The so-called canonical 1-factorization can be used for even and odd n. For even n also the so-called binary 1-factorization can be used where the teams are partitioned into 2 groups. Here it must be distinguished whether n is divisible by 4 or not.
- n even: Applet canonical 1-factorization
- n even, n=4k: Applet binary 1-factorization
- n even, n=4k+2: Applet binary 1-factorization
- n odd: Applet canonical 1-factorization
Single round robin tournaments with a minimum number of breaks
In these tournaments additionally for each match it has to be decided where it takes place (home or away). The objective is to minimize breaks (i.e. to avoid a large number of consecutive home or away matches for the teams). The minimum number of breaks is n-2 for even n and 0 for odd n.- n even: Applet directed canonical 1-factorization (n-2 breaks)
- n even, n=4k: Applet directed binary 1-factorization (n-2 breaks)
- n odd: Applet directed canonical 1-factorization (0 breaks)
Double round robin tournaments with a minimum number of breaks
In a double round robin tournament each team plays against each other team exactly twice. The tournament is divided into two half series, where in each half series each team plays against each other team (once at home, once away). The objective is to minimize breaks (i.e. to avoid consecutive home or away matches for the teams). In so-called mirrored tournaments the rounds of the second half series are scheduled in the same order as in the first half series (then the minimum number of breaks is 3(n-2)). In the so-called English system the first round of the second half series is the same as the last round of the first half series, afterwards the rounds are scheduled in the same order as in the first half series. This system ensures that only 2(n-2) breaks are needed.- n even: Applet mirrored tournament (3(n-2) breaks)
- n even: Applet English system (2(n-2) breaks)
Single round robin tournaments on a single court minimizing waiting times
In these tournaments for an odd number of teams every team plays exactly two matches in each round and all matches have to be scheduled consecutively on a single court. The objective is to minimize waiting times for the teams between their two matches. It is distinguished whether zero waiting times are allowed or not.- n odd, zero waiting times not allowed: Applet Hamiltonian 2-factorization
- n odd, zero waiting times allowed: Applet Oberwolfach 2-factorization
- n even, zero waiting times allowed: Applet Hamiltonian path factorization