{"article_type":"original","publication_status":"published","day":"05","date_published":"2023-05-05T00:00:00Z","license":"https://creativecommons.org/licenses/by/4.0/","date_created":"2023-05-21T22:01:05Z","doi":"10.37236/11471","issue":"2","language":[{"iso":"eng"}],"citation":{"short":"M. Anastos, Electronic Journal of Combinatorics 30 (2023).","ista":"Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21.","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>.","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.","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>","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>.","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>"},"external_id":{"isi":["000988285500001"],"arxiv":["2105.13828"]},"title":"A note on long cycles in sparse random graphs","status":"public","_id":"13042","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-01T14:44:52Z","year":"2023","type":"journal_article","ddc":["510"],"file_date_updated":"2023-05-22T07:43:19Z","volume":30,"oa_version":"Published Version","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"P2.21","abstract":[{"lang":"eng","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→∞."}],"has_accepted_license":"1","oa":1,"quality_controlled":"1","scopus_import":"1","publication":"Electronic Journal of Combinatorics","intvolume":"        30","file":[{"date_updated":"2023-05-22T07:43:19Z","checksum":"6269ed3b3eded6536d3d9d6baad2d5b9","access_level":"open_access","success":1,"file_name":"2023_JourCombinatorics_Anastos.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_id":"13046","date_created":"2023-05-22T07:43:19Z","file_size":448736}],"article_processing_charge":"No","acknowledgement":"We would like to thank the reviewers for their helpful comments and remarks.","month":"05","publication_identifier":{"eissn":["1077-8926"]},"department":[{"_id":"MaKw"}],"author":[{"full_name":"Anastos, Michael","last_name":"Anastos","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael"}],"publisher":"Electronic Journal of Combinatorics","isi":1}