{"quality_controlled":"1","abstract":[{"text":"We present CertifyHAM, a deterministic algorithm that takes a graph G as input and either finds a Hamilton cycle of G or outputs that such a cycle does not exist. If G ∼ G(n, p) and p ≥\r\n100 log n/n then the expected running time of CertifyHAM is O(n/p) which is best possible. This improves upon previous results due to Gurevich and Shelah, Thomason and Alon, and\r\nKrivelevich, who proved analogous results for p being constant, p ≥ 12n −1/3 and p ≥ 70n\r\n−1/2 respectively.","lang":"eng"}],"year":"2022","department":[{"_id":"MaKw"}],"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":"2022-October","date_updated":"2023-08-04T09:37:56Z","ec_funded":1,"conference":{"name":"FOCS: Symposium on Foundations of Computer Science","location":"Denver, CO, United States","start_date":"2022-10-31","end_date":"2022-11-03"},"acknowledgement":"This project has received funding from the European Union’s Horizon 2020\r\nresearch and innovation programme under the Marie Skłodowska-Curie grant\r\nagreement No 101034413","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"type":"conference","title":"Solving the Hamilton cycle problem fast on average","citation":{"mla":"Anastos, Michael. “Solving the Hamilton Cycle Problem Fast on Average.” <i>63rd Annual IEEE Symposium on Foundations of Computer Science</i>, vol. 2022–October, Institute of Electrical and Electronics Engineers, 2022, pp. 919–30, doi:<a href=\"https://doi.org/10.1109/FOCS54457.2022.00091\">10.1109/FOCS54457.2022.00091</a>.","ista":"Anastos M. 2022. Solving the Hamilton cycle problem fast on average. 63rd Annual IEEE Symposium on Foundations of Computer Science. FOCS: Symposium on Foundations of Computer Science vol. 2022–October, 919–930.","short":"M. Anastos, in:, 63rd Annual IEEE Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers, 2022, pp. 919–930.","chicago":"Anastos, Michael. “Solving the Hamilton Cycle Problem Fast on Average.” In <i>63rd Annual IEEE Symposium on Foundations of Computer Science</i>, 2022–October:919–30. Institute of Electrical and Electronics Engineers, 2022. <a href=\"https://doi.org/10.1109/FOCS54457.2022.00091\">https://doi.org/10.1109/FOCS54457.2022.00091</a>.","apa":"Anastos, M. (2022). Solving the Hamilton cycle problem fast on average. In <i>63rd Annual IEEE Symposium on Foundations of Computer Science</i> (Vol. 2022–October, pp. 919–930). Denver, CO, United States: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/FOCS54457.2022.00091\">https://doi.org/10.1109/FOCS54457.2022.00091</a>","ama":"Anastos M. Solving the Hamilton cycle problem fast on average. In: <i>63rd Annual IEEE Symposium on Foundations of Computer Science</i>. Vol 2022-October. Institute of Electrical and Electronics Engineers; 2022:919-930. doi:<a href=\"https://doi.org/10.1109/FOCS54457.2022.00091\">10.1109/FOCS54457.2022.00091</a>","ieee":"M. Anastos, “Solving the Hamilton cycle problem fast on average,” in <i>63rd Annual IEEE Symposium on Foundations of Computer Science</i>, Denver, CO, United States, 2022, vol. 2022–October, pp. 919–930."},"doi":"10.1109/FOCS54457.2022.00091","author":[{"id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","full_name":"Anastos, Michael","first_name":"Michael","last_name":"Anastos"}],"publisher":"Institute of Electrical and Electronics Engineers","oa_version":"None","publication_identifier":{"isbn":["9781665455190"],"issn":["0272-5428"]},"month":"12","date_published":"2022-12-01T00:00:00Z","article_processing_charge":"No","publication_status":"published","_id":"12432","publication":"63rd Annual IEEE Symposium on Foundations of Computer Science","day":"01","status":"public","date_created":"2023-01-29T23:00:59Z","scopus_import":"1","external_id":{"isi":["000909382900084"]},"language":[{"iso":"eng"}],"page":"919-930"}