Shortest-Weight paths in random regular graphs

Hamed Amini, Yuval Peres

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Consider a random regular graph with degree d and of size n. Assign to each edge an independent and identically distributed exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the shortest-weight paths between a fixed vertex and all the other vertices, as well as between any pair of vertices. Namely, for any fixed d ≥ 3, we show that the longest of these shortest-weight paths has aboutαlog n edges, where α is the unique solution of the equation α (d.2/d.1α) . α = d.3 d.2 for α > d.1/d.2.

Original languageEnglish (US)
Pages (from-to)656-672
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number2
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • First passage percolation
  • Shortest-weight paths
  • Weighted random graphs

ASJC Scopus subject areas

  • Mathematics(all)

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