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

Abstract

Let 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 (mod 16) 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 (mod 48) with frac(n, 2) prime, OP (F) has a solution for any 2-regular graph F of order n. © 2009 Elsevier Inc. All rights reserved.