Edge disjoint Hamilton cycles in sparse random graphs of minimum degree atleast k

Let G(n,m,k) denote the space of simple graphs with n vertices, m edges, an d minimum degree at least k, each graph G being equiprobable. Let G have pr operty A(k), if G contains [(k - 1)/2] edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size [n/2]. We prove that , for k greater than or equal to 3, there is a constant C-k such that if 2m greater than or equal to C(k)n then A(k) occurs in G(n,m,k) with probabili ty tending to 1 as n --> infinity. (C) 2000 John Wiley & Sons, Inc.