{"year":"2023","intvolume":"        30","volume":30,"ddc":["510"],"file_date_updated":"2023-05-22T07:43:19Z","isi":1,"acknowledgement":"We would like to thank the reviewers for their helpful comments and remarks.","external_id":{"arxiv":["2105.13828"],"isi":["000988285500001"]},"publication_identifier":{"eissn":["1077-8926"]},"publication":"Electronic Journal of Combinatorics","author":[{"full_name":"Anastos, Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","last_name":"Anastos","first_name":"Michael"}],"has_accepted_license":"1","doi":"10.37236/11471","article_number":"P2.21","_id":"13042","language":[{"iso":"eng"}],"citation":{"ieee":"M. Anastos, “A note on long cycles in sparse random graphs,” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 2. Electronic Journal of Combinatorics, 2023.","mla":"Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 2, P2.21, Electronic Journal of Combinatorics, 2023, doi:<a href=\"https://doi.org/10.37236/11471\">10.37236/11471</a>.","short":"M. Anastos, Electronic Journal of Combinatorics 30 (2023).","chicago":"Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href=\"https://doi.org/10.37236/11471\">https://doi.org/10.37236/11471</a>.","apa":"Anastos, M. (2023). A note on long cycles in sparse random graphs. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/11471\">https://doi.org/10.37236/11471</a>","ista":"Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21.","ama":"Anastos M. A note on long cycles in sparse random graphs. <i>Electronic Journal of Combinatorics</i>. 2023;30(2). doi:<a href=\"https://doi.org/10.37236/11471\">10.37236/11471</a>"},"article_type":"original","publisher":"Electronic Journal of Combinatorics","scopus_import":"1","oa_version":"Published Version","oa":1,"date_created":"2023-05-21T22:01:05Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","title":"A note on long cycles in sparse random graphs","status":"public","month":"05","article_processing_charge":"No","date_updated":"2023-08-01T14:44:52Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","file":[{"content_type":"application/pdf","file_name":"2023_JourCombinatorics_Anastos.pdf","creator":"dernst","access_level":"open_access","relation":"main_file","checksum":"6269ed3b3eded6536d3d9d6baad2d5b9","file_id":"13046","success":1,"file_size":448736,"date_created":"2023-05-22T07:43:19Z","date_updated":"2023-05-22T07:43:19Z"}],"day":"05","department":[{"_id":"MaKw"}],"abstract":[{"text":"Let Lc,n denote the size of the longest cycle in G(n, c/n),c >1 constant.  We show that there exists a continuous function f(c) such that Lc,n/n→f(c) a.s.  for c>20,  thus  extending  a  result  of  Frieze  and  the  author  to  smaller  values  of c. Thereafter,  for c>20,  we  determine  the  limit  of  the  probability  that G(n, c/n)contains  cycles  of  every  length  between  the  length  of  its  shortest  and  its  longest cycles as n→∞.","lang":"eng"}],"publication_status":"published","date_published":"2023-05-05T00:00:00Z","issue":"2"}