{"publication_identifier":{"eissn":["1077-8926"]},"month":"10","doi":"10.37236/10794","publication":"The Electronic Journal of Combinatorics","date_published":"2022-10-21T00:00:00Z","article_number":"P4.13","quality_controlled":"1","department":[{"_id":"MaKw"}],"intvolume":"        29","license":"https://creativecommons.org/licenses/by-nd/4.0/","scopus_import":"1","article_processing_charge":"No","date_updated":"2023-08-04T10:29:18Z","keyword":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"],"volume":29,"day":"21","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","text":"Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.&#x0D;\r\nOur main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$."}],"oa":1,"publisher":"The Electronic Journal of Combinatorics","file_date_updated":"2023-01-30T11:45:13Z","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"has_accepted_license":"1","oa_version":"Published Version","publication_status":"published","author":[{"id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver","first_name":"Oliver","last_name":"Cooley"},{"full_name":"Kang, Mihyun","last_name":"Kang","first_name":"Mihyun"},{"last_name":"Zalla","first_name":"Julian","full_name":"Zalla, Julian"}],"ddc":["510"],"issue":"4","language":[{"iso":"eng"}],"acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","date_created":"2023-01-16T10:03:57Z","_id":"12286","file":[{"date_updated":"2023-01-30T11:45:13Z","date_created":"2023-01-30T11:45:13Z","success":1,"checksum":"00122b2459f09b5ae43073bfba565e94","file_size":626953,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_id":"12462","file_name":"2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf","creator":"dernst"}],"status":"public","citation":{"chicago":"Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2022. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>.","ista":"Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13.","mla":"Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4, P4.13, The Electronic Journal of Combinatorics, 2022, doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>.","short":"O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29 (2022).","ama":"Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. 2022;29(4). doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>","apa":"Cooley, O., Kang, M., &#38; Zalla, J. (2022). Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>","ieee":"O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4. The Electronic Journal of Combinatorics, 2022."},"type":"journal_article","title":"Loose cores and cycles in random hypergraphs","year":"2022","external_id":{"isi":["000876763300001"]},"isi":1}