Abstract
We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let π i be thei th vertex encountered by DFS andL(i, m, n) be the height of π i in the corresponding DFS tree. We show that ifi/n→α asn→∞, then there exists a constanta(α,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(α,m) asn→∞. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.
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