{"id":"https://openalex.org/W4380551813","doi":"https://doi.org/10.48550/arxiv.2306.06435","title":"Linear saturation numbers of Berge-$C_3$ and Berge-$C_4$","display_name":"Linear saturation numbers of Berge-$C_3$ and Berge-$C_4$","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4380551813","doi":"https://doi.org/10.48550/arxiv.2306.06435"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2306.06435","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":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/2306.06435","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019433999","display_name":"Cynthia Wang","orcid":"https://orcid.org/0000-0001-6414-3228"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Changxin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071584772","display_name":"Junxue Zhang","orcid":"https://orcid.org/0000-0001-6926-7801"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Junxue","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":67},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9936,"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":0.9936,"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/T10849","display_name":"Finite Group Theory Research","score":0.9716,"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/T11130","display_name":"Coding theory and cryptography","score":0.9662,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/hypergraph","display_name":"Hypergraph","score":0.9756355},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.6062924}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.9756355},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8321444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7325595},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.6062924},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.584014},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.51570207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42394635},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.18455818},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06257075}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2306.06435","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":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.06435","pdf_url":"http://arxiv.org/pdf/2306.06435","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2306.06435","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2306.06435","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":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4376608938","https://openalex.org/W4376608589","https://openalex.org/W4300037846","https://openalex.org/W4288275998","https://openalex.org/W3138003926","https://openalex.org/W2963081352","https://openalex.org/W2558716804","https://openalex.org/W1630514295","https://openalex.org/W1537073411"],"abstract_inverted_index":{"The":[0],"linear":[1,21,47,77,100,144],"saturation":[2,93,101],"number":[3,7,15,154],"$sat^{lin}_k(n,\\mathcal{F})$":[4],"(linear":[5],"extremal":[6,78],"$ex^{lin}_k(n,\\mathcal{F})$)":[8],"of":[9,16,18,27,35,53,80,89,97,103,155,157],"$\\mathcal{F}$":[10,28],"is":[11,44,61,106],"the":[12,33,41,64,76,87,95,99,124,153],"minimum":[13],"(maximum)":[14],"hyperedges":[17,156],"an":[19,133],"$n$-vertex":[20],"$k$-uniform":[22,48],"hypergraph":[23,43,49,55],"containing":[24],"no":[25],"member":[26],"as":[29],"a":[30,46,51,149],"subgraph,":[31],"but":[32],"addition":[34],"any":[36,118,141],"new":[37],"hyperedge":[38],"such":[39],"that":[40,113],"result":[42],"still":[45],"creates":[50],"copy":[52],"some":[54],"in":[56,71,92],"$\\mathcal{F}$.":[57],"Determining":[58],"$ex_3^{lin}(n$,":[59],"Berge-$C_3$)":[60],"equivalent":[62],"to":[63],"famous":[65],"(6,3)-problem,":[66],"which":[67],"has":[68],"been":[69],"settled":[70],"1976.":[72],"Since":[73],"then,":[74],"determining":[75,98],"numbers":[79,102],"Berge":[81,104],"cycles":[82,105],"was":[83],"extensively":[84],"studied.":[85],"As":[86],"counterpart":[88],"this":[90,109],"problem":[91,96],"problems,":[94],"considered.":[107],"In":[108,129],"paper,":[110],"we":[111,131,147],"prove":[112],"$sat^{lin}_k$($n$,":[114],"Berge-$C_t)\\ge":[115],"\\big\\lfloor\\frac{n-1}{k-1}\\big\\rfloor$":[116],"for":[117,136,140,152],"integers":[119],"$k\\ge3$,":[120],"$t\\ge":[121],"3$,":[122],"and":[123,139],"equality":[125],"holds":[126],"if":[127],"$t=3$.":[128],"addition,":[130],"provide":[132],"upper":[134],"bound":[135,151],"$sat^{lin}_3(n,$":[137],"Berge-$C_4)$":[138],"disconnected":[142],"Berge-$C_4$-saturated":[143],"3-uniform":[145],"hypergraph,":[146],"give":[148],"lower":[150],"it.":[158]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4380551813","counts_by_year":[],"updated_date":"2025-01-06T06:25:26.946960","created_date":"2023-06-14"}