Hamilton cycles in random gra phs with a fixed degree sequence

Colin Cooper*, Alan Frieze, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let d = d1 ≤ d2 ≤ ≤ dn be a nondecreasing sequence of n positive integers whose sum is even. Let G n,d denote the set of graphs with vertex set [n] = {1, 2,⋯, n} in which the degree of vertex i is di. Let Gn,d be chosen uniformly at random from Gn,d. It will be apparent from section 4.3 that all of the sequences we are considering will be graphic. We give a condition on d under which we can show that whp Gn d is Hamiltonian. This condition is satisfied by graphs with exponential tails as well those with power law tails.

Original languageEnglish
Pages (from-to)558-569
Number of pages12
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 2010


  • Fixed degree sequence
  • Hamilton cycles
  • Random graphs


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