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 -