Covering the edges of digraphs in and with directed cuts

For nonnegative integers k and l , let D ( k , l ) denote the family of digraphs in which every vertex has either indegree at most k or outdegree at most l . In this paper we prove that the edges of every digraph in D ( 3 , 3 ) and D ( 4 , 4 ) can be covered by at most five directed cuts and present an example in D ( 3 , 3 ) showing that this result is best possible.