Optimal covers with Hamilton cycles in random graphs

A packing of a graph G with Hamilton cycles is a set of edge-disjoint Hamilton cycles in G. Such packings have been studied intensively and recent results imply that a largest packing of Hamilton cycles in G (n,p) a.a.s. has size aOES delta(G (n,p) )/2aOE <. Glebov, Krivelevich and Szab recently initiated research on the 'dual' problem, where one asks for a set of Hamilton cycles covering all edges of G. Our main result states that for , a.a.s. the edges of G (n,p) can be covered by aOEI" (G (n,p) )/2aOE parts per thousand Hamilton cycles. This is clearly optimal and improves an approximate result of Glebov, Krivelevich and Szab, which holds for p a parts per thousand yen n (-1+E >). Our proof is based on a result of Knox, Kuhn and Osthus on packing Hamilton cycles in pseudorandom graphs.