Optimal packings of Hamilton cycles in sparse random graphs
  We prove that there exists a positive constant \epsilon such that if \log n / n \le p \le n^{-1+\epsilon}, then asymptotically almost surely the random graph G ~ G(n,p) contains a collection of \lfloor \delta(G)/2 \rfloor edge-disjoint Hamilton cycles. 
Michael Krivelevich and Wojciech Samotij
math.CO