Cycle packings in graphs and digraphs (Q1910593)

A directed cycle packing in a digraph \(D\) is a subdigraph \(\mathcal C\) whose components are directed cycles. The size of \(\mathcal C\), as usual, is the number of arcs in \(\mathcal C\). A directed cycle packing \(\mathcal C\) is maximal if the subgraph induced by \(D\) on \(V(D)- V({\mathcal C})\) is acyclic; while it is maximum if no other directed cycle packing has size larger than the size of \(\mathcal C\). The author proves that for any directed multigraph \(D\), there is a vertex of \(D\) which lies in every maximum directed cycle packing of \(D\). She then points out that the corresponding problem for graphs is unsettled.