Pancyclic Hamilton cycles in random graphs (Q1182576)

The author proves that the threshold probability for a Hamiltonian cycle in a random graph is also the threshold probability for the graph to be pancyclic. In fact, the author describes a Hamiltonian cycle such that a cycle of any other length can be obtained fromt the Hamiltonian cycle by adding only two edges (and then deleting some edges of the Hamiltonian cycle). It is conjectured that ``two edges'' can be replaced by ``one edge''.