Some Results on the Oberwolfach Problem

The well‐known Oberwolfach problem is to show that it is possible to 2‐factorize K n ( n odd) or K n less a 1‐factor ( n even) into predetermined 2‐factors, all isomorphic to each other; a few exceptional cases where it is not possible are known. A completely new technique is introduced that enables it to be shown that there is a solution when each 2‐factor consists of k r ‐cycles and one ( n − kr )‐cycle for all n ⩾ 6 kr −1. Solutions are also given (with three exceptions) for all possible values of n when there is one r ‐cycle, 3 ⩽ r ⩽ 9, and one ( n − r )‐cycle, or when there are two r ‐cycles, 3 ⩽ r ⩽ 4, and one ( n −2 r )‐cycle.