Speaker: Brett Stevens (Carleton University)

Time and Place: 13 January 2006, 13:00, HP4369, Herzberg building, Carleton University

Title:   Maximally Pair Separated Round Robin Tournaments: Ordering the Blocks of a Design

Abstract:

In a Round Robin Tournament with multiple edges, we can ask that we schedule the successive games between any given pair as far apart in time as possible. We show that for a cyclic $n$ day, $\lambda = 2$, tournament schedule on $n$ players it is impossible to ask that successive games for the same pair be at least $\lfloor n/2 \rfloor$ days apart. However we also show that if we allow a small number to be separated by $\lfloor(n-2)/2 \rfloor$ days apart, then such a schedule is possible. These orderings fit into an interesting unifying framework that connects designs and Gray codes and brings together quite a few previously known results.