Conditioned random digraphs with m=cn edges and min in/out-degree at least k+1 contain k edge-disjoint Hamilton cycles w.h.p. for large enough c depending on k.
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Edge disjoint Hamilton cycles in random digraphs of constant minimum degree
Conditioned random digraphs with m=cn edges and min in/out-degree at least k+1 contain k edge-disjoint Hamilton cycles w.h.p. for large enough c depending on k.