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Balister [Combin. Probab. Comput. 12 (2003) , 1-15] gave a necessary and sufficient condition for a complete multigraph r K n to be arbitrarily decomposable into closed trails of prescribed lengths. In this article we solve the corresponding problem showing that the multigraphs r K n are arbitrarily decomposable into open trails.dblp:journals/ajc/CichaczG08 fatcat:ptqd3evpazdqnhgcmwy3eqjdxy