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For everyk  ⩾  3   $$ k\geqslant 3 $$   , we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of length     k   $$ k $$   . This solves a conjecture of Kohayakawa, Morris and the last two authors.

Counting orientations of random graphs with no directed k ‐cycles