{"id":"https://openalex.org/W4416118520","doi":"https://doi.org/10.37236/14165","title":"Supersaturation of Odd Linear Cycles","display_name":"Supersaturation of Odd Linear Cycles","publication_year":2026,"publication_date":"2026-06-05","ids":{"openalex":"https://openalex.org/W4416118520","doi":"https://doi.org/10.37236/14165"},"language":"en","primary_location":{"id":"doi:10.37236/14165","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14165","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p49/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p49/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120543976","display_name":"Lirong Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lirong Deng","raw_affiliation_strings":["Beijing Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jie Han","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Han","raw_affiliation_strings":["Beijing Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044048416","display_name":"Jiaxi Nie","orcid":"https://orcid.org/0000-0002-2657-1675"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiaxi Nie","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005628569","display_name":"Sam Spiro","orcid":"https://orcid.org/0000-0001-5715-1940"},"institutions":[{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sam Spiro","raw_affiliation_strings":["Department of Mathematics, Georgia State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Georgia State University","institution_ids":["https://openalex.org/I181565077"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08178792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/supersaturation","display_name":"Supersaturation","score":0.39980000257492065},{"id":"https://openalex.org/keywords/conditioning","display_name":"Conditioning","score":0.33970001339912415},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.32190001010894775},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.290800005197525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6328999996185303},{"id":"https://openalex.org/C200447597","wikidata":"https://www.wikidata.org/wiki/Q334104","display_name":"Supersaturation","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3720000088214874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3698999881744385},{"id":"https://openalex.org/C45262634","wikidata":"https://www.wikidata.org/wiki/Q5159291","display_name":"Conditioning","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32670000195503235},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3043000102043152},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2612999975681305}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/14165","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14165","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p49/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2504.05116","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.05116","pdf_url":"https://arxiv.org/pdf/2504.05116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2504.05116","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.05116","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/14165","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14165","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p49/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3977112998","display_name":null,"funder_award_id":"12371341","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8331563887","display_name":null,"funder_award_id":"DMS-2202730","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8728984716","display_name":"PostDoctoral Research Fellowship","funder_award_id":"2202730","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416118520.pdf","grobid_xml":"https://content.openalex.org/works/W4416118520.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"An":[0],"$r$-uniform":[1],"linear":[2],"cycle":[3],"of":[4,42,49,68],"length":[5],"$\\ell$,":[6],"denoted":[7],"by":[8],"$C^r_{\\ell}$,":[9],"is":[10],"an":[11],"$r$-graph":[12,32],"with":[13,34,60],"$\\ell$":[14],"edges":[15,36,62],"$e_1,e_2,\\dots,e_{\\ell}$":[16],"where":[17],"$e_i=\\{v_{(r-1)(i-1)},v_{(r-1)(i-1)+1},\\dots,v_{(r-1)i}\\}$":[18],"(here":[19],"$v_0=v_{(r-1)\\ell}$).":[20],"For":[21],"$0&lt;\\delta&lt;1$":[22],"and":[23,63],"$n$":[24],"sufficiently":[25],"large,":[26],"we":[27,53],"show":[28,54],"that":[29,55],"every":[30],"$n$-vertex":[31,58],"$G$":[33],"$n^{r-\\delta}$":[35,61],"contains":[37],"at":[38,64],"least":[39],"$n^{(r-1)(2\\ell+1)-\\delta(2\\ell+1+\\frac{4\\ell-1}{(r-1)(2\\ell+1)-3})-o(1)}$":[40],"copies":[41,67],"$C^r_{2\\ell+1}$.":[43,69],"Further,":[44],"conditioning":[45],"on":[46],"the":[47],"existence":[48],"dense":[50],"high-girth":[51],"hypergraphs,":[52],"there":[56],"exists":[57],"$r$-graphs":[59],"most":[65],"$n^{(r-1)(2\\ell+1)-\\delta(2\\ell+1+\\frac{1}{(r-1)\\ell-1})+o(1)}$":[66]},"counts_by_year":[],"updated_date":"2026-06-07T06:13:29.825681","created_date":"2025-10-10T00:00:00"}
