Embedding spanning trees in random graphs

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that if T is a tree on n vertices with maximum degree Δ and the edge probability p(n) satisfies np ≥ C max{Δ log n, n } for some constant ∈ > 0, then with high probability the random graph G(n, p) contains a copy of T. The obtained bound on the edge probability is shown to be essentially tight for Δ = n Θ(1).

Original languageEnglish
Pages (from-to)1495-1500
Number of pages6
JournalSIAM Journal on Discrete Mathematics
Volume24
Issue number4
DOIs
StatePublished - 2010

Keywords

  • Embedding
  • Random graphs
  • Spanning trees

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