TY - JOUR

T1 - Hamilton cycles in random subgraphs of pseudo-random graphs

AU - Frieze, Alan

AU - Krivelevich, Michael

N1 - Funding Information:
∗Corresponding author. E-mail addresses: alan@random.math.cmu.edu (A. Frieze), krivelev@math.tau.ac.il (M. Krivelevich). 1Supported in part by NSF grant CCR-9818411. 2Supported in part by USA–Israel BSF Grant 99-0013 and by a Bergmann Memorial Grant.

PY - 2002/9/28

Y1 - 2002/9/28

N2 - Given an r-regular graph G on n vertices with a Hamilton cycle, order its edges randomly and insert them one by one according to the chosen order, starting from the empty graph. We prove that if the eigenvalue of the adjacency matrix of G with the second largest absolute value satisfies λ = o(r5/2/(n3/2(log n)3/2)), then for almost all orderings of the edges of G at the very moment τ* when all degrees of the obtained random subgraph Ht* of G become at least two, Hτ* has a Hamilton cycle. As a consequence we derive the value of the threshold for the appearance of a Hamilton cycle in a random subgraph of a pseudo-random graph G, satisfying the above stated condition.

AB - Given an r-regular graph G on n vertices with a Hamilton cycle, order its edges randomly and insert them one by one according to the chosen order, starting from the empty graph. We prove that if the eigenvalue of the adjacency matrix of G with the second largest absolute value satisfies λ = o(r5/2/(n3/2(log n)3/2)), then for almost all orderings of the edges of G at the very moment τ* when all degrees of the obtained random subgraph Ht* of G become at least two, Hτ* has a Hamilton cycle. As a consequence we derive the value of the threshold for the appearance of a Hamilton cycle in a random subgraph of a pseudo-random graph G, satisfying the above stated condition.

KW - Hamilton cycles

KW - Pseudo-random graphs

KW - Random graphs

UR - http://www.scopus.com/inward/record.url?scp=31244434954&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(01)00464-2

DO - 10.1016/S0012-365X(01)00464-2

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AN - SCOPUS:31244434954

SN - 0012-365X

VL - 256

SP - 137

EP - 150

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-2

ER -