The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph

Asaf Ferber, Kaarel Haenni, Vishesh Jain

Let $H_1,\dots ,H_k$ be Hamilton cycles in $K_n$, chosen independently and uniformly at random. We show, for $k=o(n^{1/100})$, that the probability of $H_1,\dots ,H_k$ being edge-d…