Directed star decompositions of directed multigraphs

AbstractAn (s,t)-directed star decomposition of a directed multigraph is a partition of the ars into directed stars, each having s arcs into the center and t arcs out of the center. We determine necessary and sufficient conditions for a directed complete multigraph to have an (s,t)-directed star decomposition. We futher determine necessary abd sufficient conditions for a regular directed symmetric graph to have such a decomposition in which each vertex is the center of the same number of stars