On Matchings and Hamiltonian Cycles in Random Graphs


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