{"abstract":[{"lang":"eng","text":"Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if p≥(logn+ω(1))/n then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically n!(p(1+o(1)))n. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically n!(logn/n(1+o(1)))n directed Hamilton cycles."}],"date_created":"2021-06-18T12:06:28Z","date_published":"2018-12-01T00:00:00Z","external_id":{"arxiv":["1708.07746"]},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","doi":"10.1002/rsa.20815","year":"2018","publisher":"Wiley","publication":"Random Structures and Algorithms","oa_version":"Preprint","month":"12","day":"01","issue":"4","language":[{"iso":"eng"}],"title":"Counting Hamilton cycles in sparse random directed graphs","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1708.07746","open_access":"1"}],"extern":"1","status":"public","article_processing_charge":"No","author":[{"last_name":"Ferber","first_name":"Asaf","full_name":"Ferber, Asaf"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","last_name":"Kwan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"}],"publication_status":"published","article_type":"original","page":"592-603","volume":53,"intvolume":"        53","scopus_import":"1","date_updated":"2023-02-23T14:01:03Z","type":"journal_article","oa":1,"_id":"9565","publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"citation":{"mla":"Ferber, Asaf, et al. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” <i>Random Structures and Algorithms</i>, vol. 53, no. 4, Wiley, 2018, pp. 592–603, doi:<a href=\"https://doi.org/10.1002/rsa.20815\">10.1002/rsa.20815</a>.","short":"A. Ferber, M.A. Kwan, B. Sudakov, Random Structures and Algorithms 53 (2018) 592–603.","ista":"Ferber A, Kwan MA, Sudakov B. 2018. Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. 53(4), 592–603.","apa":"Ferber, A., Kwan, M. A., &#38; Sudakov, B. (2018). Counting Hamilton cycles in sparse random directed graphs. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.20815\">https://doi.org/10.1002/rsa.20815</a>","ieee":"A. Ferber, M. A. Kwan, and B. Sudakov, “Counting Hamilton cycles in sparse random directed graphs,” <i>Random Structures and Algorithms</i>, vol. 53, no. 4. Wiley, pp. 592–603, 2018.","ama":"Ferber A, Kwan MA, Sudakov B. Counting Hamilton cycles in sparse random directed graphs. <i>Random Structures and Algorithms</i>. 2018;53(4):592-603. doi:<a href=\"https://doi.org/10.1002/rsa.20815\">10.1002/rsa.20815</a>","chicago":"Ferber, Asaf, Matthew Alan Kwan, and Benny Sudakov. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” <i>Random Structures and Algorithms</i>. Wiley, 2018. <a href=\"https://doi.org/10.1002/rsa.20815\">https://doi.org/10.1002/rsa.20815</a>."}}