A generalization of the Oberwolfach problem and C t ‐factorizations of complete equipartite graphs

We consider the following generalization of the Oberwolfach problem: “At a gathering there are n delegations each having m people. Is it possible to arrange a seating of mn people present at s round tables ${T}_{1},{T}_{2},\ldots,{T}_{s}$ (where $T_i$ can accommodate $t_i \ge 3$ people and $\sum t_i=mn$ ) for k different meals so that each person has every other person not in the same delegation for a neighbour exactly once?”. We will concentrate on the case when all tables accommodate the same number t of people, give a complete solution for t even and settle most cases for t odd. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 42–49, 2000