Cycle decompositions of complete multigraphs

Abstract

It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with λ edges joining each pair of distinct vertices into m-cycles, or into m-cycles and a perfect matching, are also sufficient. This result follows as an easy consequence of more general results which are obtained on decompositions of complete multigraphs into cycles of varying lengths. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:42-69, 2010