Complete solutions to the Oberwolfach problem for an infinite set of orders

AbstractLet n⩾3 and let F be a 2-regular graph of order n. The Oberwolfach problem OP(F) asks for a 2-factorisation of Kn if n is odd, or of Kn−I if n is even, in which each 2-factor is isomorphic to F. We show that there is an infinite set N of primes congruent to 1(mod16) such that OP(F) has a solution for any 2-regular graph F of order n∈N. We also show that for each of the infinitely many n≡10(mod48) with n2 prime, OP(F) has a solution for any 2-regular graph F of order n