On depth first search strees inm-out digraphs


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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Stephen Suen, W.C. On depth first search strees inm-out digraphs. Combinatorica 13, 209–229 (1993). https://doi.org/10.1007/BF01303205

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AMS subject classification code (1991)

  • 05 C 20
  • 68 R 10