TY - JOUR

T1 - On the number of Hamilton cycles in sparse random graphs

AU - Glebov, Roman

AU - Krivelevich, Michael

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Hamilton cycles

KW - Number of Hamilton cycles

KW - Random graphs

UR - http://www.scopus.com/inward/record.url?scp=84876949951&partnerID=8YFLogxK

U2 - 10.1137/120884316

DO - 10.1137/120884316

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AN - SCOPUS:84876949951

SN - 0895-4801

VL - 27

SP - 27

EP - 42

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -