The Oberwolfach problem with loving couples

Abstract We generalize the well‐known Oberwolfach problem posed by Ringel in 1967. We suppose to have couples (here is an even integer) and suppose that they have to be seated for several nights at round tables in such a way that each person seats next to his partner exactly times and next to every other person exactly once. We call this problem the Oberwolfach problem with loving couples. When , the problem coincides with the so‐called spouse‐avoiding variant, which was introduced by Huang, Kotzig, and Rosa in 1979. While if either or equals the number of nights, it corresponds to the spouse‐loving variant or to the Honeymoon variant, which was recently studied by Bolohan et al. and by Lepine and Sajna, respectively. In this paper, for each possible choice of , we construct many classes of solutions to the Oberwolfach problem with loving couples. We also obtain new solutions to the Honeymoon variant.