Abstract
In the previous chapters, we considered various properties of cycles in digraphs. In this chapter, we consider the question of how few vertices have to be deleted to get rid of all cycles. We will also consider the arc version of this question (i.e., to destroy all cycles we delete arcs rather than vertices). The last question leads us to the notion of an ‘optimal’ ordering of a digraph which is of interest in various applications. We will see that the minimum number of vertices (arcs) required to destroy all cycles is related to the maximum number of vertex-disjoint (arc-disjoint) cycles in the digraph under consideration. We will also consider the question of decreasing the number of cycles by reversing arcs.
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