Title: Optimally packing Hamilton cycles in random digraphs
Abstract:
At most how many edge-disjoint Hamilton cycles does a given directed graph contain?
It is easy to see that one cannot pack more than the minimum in-degree or the minimum out-degree of the digraph. We show that in the random directed graph D(n,p) one can pack precisely this many edge-disjoint Hamilton cycles, with high probability, given that p is at least the Hamiltonicity threshold, up to a polylog factor.
Based on a joint work with Asaf Ferber.