On a variation of the Oberwolfach problem

Abstract

We consider the following "spouse-avoiding" variant of the Oberwolfach problem (briefly NOP): "At a gathering there are n couples. Is it possible to arrange a seating for the 2n people present at s round tables T1,T2,...,Ts (where Ti can accomodate ki ≥ 3 people and Σki=2n) for m different meals so that each person has every other person except his spouse for a neighbour exactly once?" We prove several results concerning the existence of solutions to NOP. In particular, we settle the cases when the tables accomodate the same "small" number of people or when there are only two tables one of them accomodating a "small" number of people or when the total number of people is "small". © 1979.