{"id":"https://openalex.org/W7203924349","doi":"https://doi.org/10.48550/arxiv.2608.20190","title":"Small circumference in regular sublinear expanders","display_name":"Small circumference in regular sublinear expanders","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203924349","doi":"https://doi.org/10.48550/arxiv.2608.20190"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20190","pdf_url":"https://arxiv.org/pdf/2608.20190","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.20190","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137626992","display_name":"Yaobin Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chen, Yaobin","raw_affiliation_strings":["Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea","institution_ids":["https://openalex.org/I4210104335"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147745568","display_name":"Hong Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Liu, Hong","raw_affiliation_strings":["Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea","institution_ids":["https://openalex.org/I4210104335"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147693103","display_name":"Xin Wei","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Wei, Xin","raw_affiliation_strings":[", Natural Science Foundation of Shandong Province ( ZR2024QA056), and China","Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", Natural Science Foundation of Shandong Province ( ZR2024QA056), and China","institution_ids":[]},{"raw_affiliation_string":"Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea","institution_ids":["https://openalex.org/I4210104335"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5140290394","display_name":"Fan Yang","orcid":"https://orcid.org/0009-0005-4570-5885","observed_orcids":["https://orcid.org/0009-0005-4570-5885"]},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yang, Fan","raw_affiliation_strings":["Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Extremal Combinatorics and Probability Group (ECOPRO) , Institute for Basic Science (IBS) , Daejeon , South Korea","institution_ids":["https://openalex.org/I4210104335"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210104335"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9994999766349792,"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":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regular-graphs","display_name":"regular graphs","score":0.546999990940094},{"id":"https://openalex.org/keywords/hamiltonian-cycles","display_name":"Hamiltonian cycles","score":0.6370000243186951},{"id":"https://openalex.org/keywords/circumference","display_name":"circumference","score":0.5419999957084656},{"id":"https://openalex.org/keywords/ramanujan-graphs","display_name":"Ramanujan graphs","score":0.8999999761581421},{"id":"https://openalex.org/keywords/biregular-graphs","display_name":"biregular graphs","score":0.8690000176429749},{"id":"https://openalex.org/keywords/vertex-separators","display_name":"vertex separators","score":0.3970000147819519}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.8971999883651733},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8486999869346619},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.7195000052452087},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.7171000242233276},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6743999719619751},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5390999913215637},{"id":"https://openalex.org/C166504685","wikidata":"https://www.wikidata.org/wiki/Q843905","display_name":"Circumference","level":2,"score":0.5006999969482422},{"id":"https://openalex.org/C185004128","wikidata":"https://www.wikidata.org/wiki/Q3011536","display_name":"Separator (oil production)","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4593000113964081},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.42480000853538513},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.3862000107765198},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C191916993","wikidata":"https://www.wikidata.org/wiki/Q362019","display_name":"Numbering","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20190","pdf_url":"https://arxiv.org/pdf/2608.20190","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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.2608.20190","doi":"https://doi.org/10.48550/arxiv.2608.20190","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20190","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.20190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20190","pdf_url":"https://arxiv.org/pdf/2608.20190","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2060818609","display_name":null,"funder_award_id":"12301447","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2765210714","display_name":null,"funder_award_id":"IBS\u2010R029\u2010C4","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326441","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203924349.pdf","grobid_xml":"https://content.openalex.org/works/W7203924349.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4391767055","https://openalex.org/W7161277500","https://openalex.org/W7171739287"],"related_works":["https://openalex.org/W7128782036","https://openalex.org/W7204599727","https://openalex.org/W7161277500","https://openalex.org/W4391767055","https://openalex.org/W4398241018","https://openalex.org/W7164026975","https://openalex.org/W2117306309","https://openalex.org/W7098202451","https://openalex.org/W7221805961","https://openalex.org/W2950684534"],"abstract_inverted_index":{"Sublinear":[0],"expansion":[1],"is":[2,69,148],"weak":[3],"enough":[4,24],"to":[5,25,185],"be":[6],"extracted":[7],"from":[8,171],"arbitrary":[9],"graphs":[10],"while":[11,192],"retaining":[12],"nearly":[13,44],"all":[14],"of":[15,43,101,110,139,152],"their":[16],"average":[17],"degree,":[18],"yet":[19],"it":[20],"has":[21,180],"proved":[22,40],"strong":[23,77],"force":[26],"global":[27],"structures":[28],"in":[29,47,75],"many":[30],"sparse":[31,125],"extremal":[32],"problems.":[33],"Letzter,":[34],"Methuku":[35],"and":[36,118,158],"Sudakov":[37],"[JLMS":[38],"2026]":[39,55],"the":[41,120,162,193],"existence":[42],"Hamilton":[45],"cycles":[46],"sufficiently":[48,65,144],"dense":[49],"regular":[50,174],"sublinear":[51,61,83],"expanders.":[52,141],"Montgomery":[53],"[ICM":[54],"subsequently":[56],"conjectured":[57],"that,":[58],"every":[59,143,197],"$d$-regular":[60,82,154],"expander":[62],"with":[63,85,156],"$d$":[64],"large":[66],"(but":[67],"constant)":[68],"Hamiltonian.":[70],"We":[71,128],"disprove":[72],"this":[73],"conjecture":[74],"a":[76,111,124,131,135],"form":[78],"by":[79],"constructing":[80],"$n$-vertex":[81,153],"expanders":[84],"$d=\\left(\\frac12+o(1)\\right)\\log^2":[86],"n$,":[87],"which":[88],"can":[89],"forbid":[90],"any":[91],"cycle":[92],"covering":[93],"an":[94,149,172,181],"arbitrarily":[95],"small":[96,145],"given":[97],"positive":[98],"constant":[99],"portion":[100],"its":[102],"vertices.":[103],"The":[104,167,187],"construction":[105,168],"blows":[106],"up":[107],"one":[108],"side":[109,122],"biregular":[112],"Ramanujan":[113],"graph":[114,183],"into":[115],"almost-complete":[116,182],"blocks":[117],"keeps":[119],"other":[121],"as":[123],"vertex":[126,179],"separator.":[127],"also":[129,169],"prove":[130],"similar":[132],"statement":[133],"for":[134],"closely":[136],"related":[137],"notion":[138],"edge":[140,190],"For":[142],"$\u03b3>0$,":[146],"there":[147],"infinite":[150],"family":[151],"$\u03b3$-edge-expanders":[155],"$d=\u0398(\u03b3^{-1})$":[157],"circumference":[159],"$O(\u03b3n)$,":[160],"matching":[161],"standard":[163],"lower":[164],"bound":[165],"$\u03a9(\u03b3n)$.":[166],"comes":[170],"expanding":[173],"core":[175,188],"such":[176],"that":[177],"each":[178],"attached":[184],"it.":[186],"guarantees":[189],"expansion,":[191],"single-vertex":[194],"attachments":[195],"confine":[196],"cycle.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-22T00:00:00"}
