SPORT TOURMANENTS WITH MINIMUM NUMBER OF TRAVELING FOR FIVE AND SIX TEAMS

Abstract

There are many sport tournaments nowadays. One type of sport traveling tournament could be considered a traveling tournament problem (TTP) or double round robin since each team has to plays against another team twice: one home game and one opponents home game. If there are n teams and each team is required to plays against every other team in the first n - 1 games, this is called a half traveling tournament problem (HTTP). If the HTTP also requires that the last n-1 games are ordered exactly like the first n- 1 games with reversed venues, then it is called a mirrored traveling tournament problem (MTTP). This research
aims to study about how to schedule the sport tournament with minimum total number of traveling of all teams in case of five and six teams. The proofs and examples of tournaments with minimum total number of traveling are presented. The result shows that the minimum total number of all team traveling for five team sport tournament is 26 and for six team sport tournament is 38. Both tournaments are considered MTTP.