Chain Lengths in Certain Random Directed Graphs

Research output: Contribution to journalArticle

Abstract

We study the random directed graph with vertex set {1, …, n} in which the directed edges (i, j) occur independently with probability cn/n for i<j and probability zero for i ⩽ j. Let Mn (resp., Ln) denote the length of the longest path (resp., longest path starting from vertex 1). When cn is bounded away from 0 and ∞ as n→∞, the asymptotic behavior of Mn was analyzed in previous work of the author and J. E. Cohen. Here, all restrictions on cn are eliminated and the asymptotic behavior of Ln is also obtained. In particular, if cn/ln(n)→∞ while cn/n→0, then both Mn/cn and Ln/cn are shown to converge in probability to the constant e.

Original languageEnglish (US)
Pages (from-to)243-253
Number of pages11
JournalRandom Structures and Algorithms
Volume3
Issue number3
DOIs
StatePublished - 1992

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Directed graphs
Chain length
Random Graphs
Directed Graph
Longest Path
Asymptotic Behavior
Vertex of a graph
Denote
Restriction
Converge
Zero

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Cite this

Chain Lengths in Certain Random Directed Graphs. / Newman, Charles.

In: Random Structures and Algorithms, Vol. 3, No. 3, 1992, p. 243-253.

Research output: Contribution to journalArticle

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