{"month":"12","day":"01","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","quality_controlled":"1","_id":"9565","page":"592-603","language":[{"iso":"eng"}],"date_updated":"2023-02-23T14:01:03Z","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1708.07746","open_access":"1"}],"extern":"1","publisher":"Wiley","intvolume":"        53","author":[{"full_name":"Ferber, Asaf","last_name":"Ferber","first_name":"Asaf"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan"},{"full_name":"Sudakov, Benny","last_name":"Sudakov","first_name":"Benny"}],"date_created":"2021-06-18T12:06:28Z","abstract":[{"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.","lang":"eng"}],"oa":1,"publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"title":"Counting Hamilton cycles in sparse random directed graphs","doi":"10.1002/rsa.20815","article_type":"original","external_id":{"arxiv":["1708.07746"]},"article_processing_charge":"No","scopus_import":"1","issue":"4","status":"public","oa_version":"Preprint","type":"journal_article","publication":"Random Structures and Algorithms","date_published":"2018-12-01T00:00:00Z","citation":{"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.","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>.","short":"A. Ferber, M.A. Kwan, B. Sudakov, Random Structures and Algorithms 53 (2018) 592–603.","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>.","ista":"Ferber A, Kwan MA, Sudakov B. 2018. Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. 53(4), 592–603.","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>","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>"},"volume":53,"year":"2018"}