Cycle packings in graphs and digraphs

A cycle packing in a (directed) multigraph is a vertex disjoint collection of (directed) elementary cycles. If D is a demiregular multidigraph we show that the arcs of D can be partitioned into Δin cycle packings — where δin is the maximum indegree of a vertex in D. We then show that the maximum length cycle packings in any digraph contain a common vertex.