Sectionable terraces and the (generalised) Oberwolfach problem Original Research Article

The generalised Oberwolfach problem requires v people to sit at s round tables of sizes l1,l2,…,ls (where l1+l2+⋯+ls=v) for successive meals in such a way that each pair of people are neighbours exactly λ times. The problem is denoted OP(λ;l1,l2,…,ls) and if λ=1, which is the original problem, this is abbreviated to OP(l1,l2,…,ls). It was known in 1892, though different terminology was then used, that a directed terrace with a symmetric sequencing for the cyclic group of order 2n can be used to solve OP(2n+1). We show how terraces with special properties can be used to solve OP(2;l1,l2) and OP(l1,l1,l2) for a wide selection of values of l1, l2 and v. We also give a new solution to OP(2;l,l) that is based on Z2l−1. Solutions to the problem are also of use in the design of experiments, where solutions for tables of equal size are called resolvable balanced circuit Rees neighbour designs.