Regular Oberwolfach problems and group sequencings

We deal with Oberwolfach factorizations of the complete graphs K-n and K-n* , which admit a regular group of automorphisms. We show that the existence of such a factorization is equivalent to the existence of a certain differe nce sequence defined on the elements of the automorphism group, or to a cer tain sequencing of the elements of that group. In the particular case of a hamiltonian factorization of the directed graph K-n*, which admits a regula r group of automorphisms G (\G \ = n - 1), we have that such a factorizatio n exists if and only if G is sequenceable. We shall demonstrate how the men tioned above (difference) sequences may be used in the construction of such factorizations. We prove also that a hamiltonian factorization of the undi rected graph K-n (n odd) which admits a regular group of automorphisms G (\ G \ = (n - 1)/2) exists if and only if n equivalent to 3 (mod 4), without f urther restrictions on the structure of G. (C) 2001 Academic Press.