(m,n)-cycle systems

Abstract

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case {m(1), m(2), ..., m(t)}=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.