Scheduling matches to allow shared transport, or how to get free tickets to your local team's home games

09/13/2016 - 12:15pm
09/13/2016 - 1:10pm
Christopher Tuffley (Massey University Manawatu)

Consider a sports tournament with two divisions, in which each team is to play every other team in the same division, in a series of home and away games, one per week. Suppose moreover that every club with a team in division 1 also has a team in division 2, but not vice versa. If both teams from two clubs A and B play each other at the same venue in the same week, then the club with the away game will be able to arrange shared transport for its two teams; otherwise, separate transport arrangements will need to be made for each travelling team. How can we arrange the schedule to maximise the number of such "common fixtures"? In January 2011 the Manawatu Rugby Union approached me with an instance of this scheduling problem, in which there were 10 teams in division one and 12 in division two. They were so pleased with the schedule I provided that they gave me free tickets to the Manawatu Turbos' home games that year. I will explain how to solve this problem for the case of 2n teams in division one and 2n+2 in division two (joint work with Wayne Burrows), so that you, too, have an opportunity to benefit a local sports league, the environment, *and* yourself through combinatorics. The talk will be accessible to those without a background in combinatorics.

Millikan 2099, Pomona College