10.1184/R1/6477569.v1
Colin Cooper
Alan Frieze
Michael Krivelevich
Hamilton cycles in random graphs with a fixed degree sequence
2010
Carnegie Mellon University
Mathematical Sciences
2010-03-01 00:00:00
article
https://kilthub.cmu.edu/articles/journal_contribution/Hamilton_cycles_in_random_graphs_with_a_fixed_degree_sequence/6477569
<p>Let d = d1 ≤ d2 ≤ · · · ≤ dn be a non-decreasing sequence of n positive integers, whose sum is even. Let Gn,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 the sequences we are considering will all 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.</p>