On the number of Hamilton cycles in sparse random graphs

Roman Glebov, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review


We prove that the number of Hamilton cycles in the random graph G(n, p) is n!pn(1+ o(1))n asymptotically almost surely (a.a.s.), provided that p ≥ ln n+ln ln n+ω(1)/n. Furthermore, we prove the hitting time version of this statement, showing that in the random graph process, the edge that creates a graph of minimum degree 2 creates (ln n/e) n(1 + o(1))n Hamilton cycles a.a.s.

Original languageEnglish
Pages (from-to)27-42
Number of pages16
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2013


  • Hamilton cycles
  • Number of Hamilton cycles
  • Random graphs

All Science Journal Classification (ASJC) codes

  • General Mathematics


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