On Matchings and Hamiltonian Cycles in Random Graphs
Abstract
Let m = ¼n log n + ½n log log n +cn. Let Λ denote the set of graphs with vertices {1, 2, …, n}, m edges and minimum degree 1. We show that if a random graph G is chosen uniformly from Λ then We also show that if a random graph G with vertices {1, 2, …, n} is constructed by randomly adding edges one at a time then, almost surely, as soon as G has degree k, G has [k/2] disjoint hamiltonian cycles plus a disjoint perfect matching if k is odd, where k is a fixed positive integer. © 1985, Elsevier Inc. All rights reserved.
Publication Title
North-Holland Mathematics Studies
Recommended Citation
Bollobás, B., & Frieze, A. (1985). On Matchings and Hamiltonian Cycles in Random Graphs. North-Holland Mathematics Studies, 118 (C), 23-46. https://doi.org/10.1016/S0304-0208(08)73611-9
