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 -