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For nonnegative integers k and l, let D(k,l) denote the set of digraphs in which every vertex has indegree at most k or outdegree at most l. In this paper, we first compare three existing upper bounds for the number of directed cuts to cover the arcs of digraphs in D(k,k) and prove that these bounds can be improved from seven to six in the case k=5,6. Further, we give a lower bound for the number...
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.
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