TY - JOUR

T1 - Hamilton cycles in random gra phs with a fixed degree sequence

AU - Cooper, Colin

AU - Frieze, Alan

AU - Krivelevich, Michael

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Fixed degree sequence

KW - Hamilton cycles

KW - Random graphs

UR - http://www.scopus.com/inward/record.url?scp=77954529092&partnerID=8YFLogxK

U2 - 10.1137/080741379

DO - 10.1137/080741379

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AN - SCOPUS:77954529092

SN - 0895-4801

VL - 24

SP - 558

EP - 569

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 2

ER -