On two Hamilton cycle problems in random graphs

Alan Frieze, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review


We study two problems related to the existence of Hamilton cycles in random graphs. The first question relates to the number of edge disjoint Hamilton cycles that the random graph Gn,pcontains. δ(G)/2 is an upper bound and we show that if p ≤ (1 + o(1)) ln n/n then this upper bound is tight whp. The second question relates to how many edges can be adversarially removed from Gn,p without destroying Hamiltonicity. We show that if p ≥ K ln n/n then there exists a constant α > 0 such that whp G - H is Hamiltonian for all choices of H as an n-vertex graph with maximum degree Δ(H) ≤ αK ln n.

Original languageEnglish
Pages (from-to)221-234
Number of pages14
JournalIsrael Journal of Mathematics
StatePublished - Aug 2008


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