{"id":"https://openalex.org/W3083306962","doi":"https://doi.org/10.37236/9061","title":"Codegree Threshold for Tiling Balanced Complete $3$-Partite $3$-Graphs and Generalized $4$-Cycles","display_name":"Codegree Threshold for Tiling Balanced Complete $3$-Partite $3$-Graphs and Generalized $4$-Cycles","publication_year":2020,"publication_date":"2020-09-04","ids":{"openalex":"https://openalex.org/W3083306962","doi":"https://doi.org/10.37236/9061","mag":"3083306962"},"language":"en","primary_location":{"id":"doi:10.37236/9061","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9061","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p47/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p47/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068315573","display_name":"Xinmin Hou","orcid":"https://orcid.org/0000-0002-7634-0250"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinmin Hou","raw_affiliation_strings":["CAS Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, PR China","School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"CAS Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101545200","display_name":"Boyuan Liu","orcid":"https://orcid.org/0009-0009-5307-1172"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Boyuan Liu","raw_affiliation_strings":["University of Science and Technology of China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100443141","display_name":"Yue Ma","orcid":"https://orcid.org/0009-0002-2299-4555"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Ma","raw_affiliation_strings":["School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068315573"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26625885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"3","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9987000226974487,"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/T11476","display_name":"Graph theory and applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/combinatorics","display_name":"Combinatorics","score":0.9120782613754272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8328484892845154},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5999885201454163},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.56276935338974},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.535677969455719},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4982318878173828},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4700181782245636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42738085985183716}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9120782613754272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8328484892845154},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5999885201454163},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.56276935338974},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.535677969455719},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4982318878173828},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4700181782245636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42738085985183716}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9061","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9061","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p47/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"}],"best_oa_location":{"id":"doi:10.37236/9061","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9061","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p47/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3083306962.pdf","grobid_xml":"https://content.openalex.org/works/W3083306962.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W830927343","https://openalex.org/W1444168583","https://openalex.org/W1861552184","https://openalex.org/W1867281446","https://openalex.org/W1923478559","https://openalex.org/W1957375148","https://openalex.org/W1994305080","https://openalex.org/W2005146019","https://openalex.org/W2014564484","https://openalex.org/W2030651378","https://openalex.org/W2053158631","https://openalex.org/W2115730400","https://openalex.org/W2137916360","https://openalex.org/W2144292514","https://openalex.org/W2183769808","https://openalex.org/W2202608853","https://openalex.org/W2217677052","https://openalex.org/W2303867231","https://openalex.org/W2523230043","https://openalex.org/W2564017106","https://openalex.org/W2585665079","https://openalex.org/W2950509301","https://openalex.org/W2953275476","https://openalex.org/W2961722459","https://openalex.org/W2962841333","https://openalex.org/W2963274279","https://openalex.org/W2963408774","https://openalex.org/W2963988718","https://openalex.org/W2963991599","https://openalex.org/W4247935778","https://openalex.org/W4285719527","https://openalex.org/W4296232596","https://openalex.org/W4302386875","https://openalex.org/W4309682749","https://openalex.org/W6687515693","https://openalex.org/W6732450347","https://openalex.org/W6764193857"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W1971174658","https://openalex.org/W2080136900","https://openalex.org/W2099195351","https://openalex.org/W2372768926","https://openalex.org/W2999799752","https://openalex.org/W2054458431","https://openalex.org/W3013576436"],"abstract_inverted_index":{"Given":[0],"two":[1],"$k$-graphs":[2,69],"$F$":[3,22,70],"and":[4,71,108,148,161,185],"$H$,":[5],"a":[6,16,54,85,130,180],"perfect":[7,55],"$F$-tiling":[8],"(also":[9],"called":[10],"an":[11],"$F$-factor)":[12],"in":[13,78,126],"$H$":[14,43],"is":[15,112,136,191,197],"set":[17,28],"of":[18,21,29,64,100,205],"vertex-disjoint":[19],"copies":[20],"that":[23,40,73,87,134,187],"together":[24],"cover":[25],"the":[26,35,61,74,97,113,117,137,175,188,198],"vertex":[27,125],"$H$.":[30],"Let":[31],"$t_{k-1}(n,":[32,65,79],"F)$":[33,66,80],"be":[34,82],"smallest":[36],"integer":[37],"$t$":[38,52],"such":[39],"every":[41],"$k$-graph":[42],"on":[44,90,145],"$n$":[45],"vertices":[46,147],"with":[47,156,202],"minimum":[48],"codegree":[49],"at":[50],"least":[51],"contains":[53],"$F$-tiling.":[56],"Mycroft":[57],"(JCTA,":[58],"2016)":[59],"determined":[60],"asymptotic":[62],"values":[63],"for":[67,170,193],"$k$-partite":[68],"conjectured":[72],"error":[75,176],"terms":[76],"$o(n)$":[77,178],"can":[81],"replaced":[83],"by":[84,106,122,129],"constant":[86],"depends":[88],"only":[89],"$F$.":[91],"In":[92],"this":[93],"paper,":[94],"we":[95,173],"determine":[96],"exact":[98],"value":[99],"$t_2(n,":[101],"K_{m,m}^{3})$,":[102],"where":[103,195],"$K_{m,m}^{3}$":[104],"(defined":[105],"Mubayi":[107],"Verstra\u00ebte,":[109],"JCTA,":[110],"2004)":[111],"3-graph":[114,144],"obtained":[115],"from":[116],"complete":[118,199],"bipartite":[119],"graph":[120],"$K_{m,m}$":[121],"replacing":[123],"each":[124,203],"one":[127],"part":[128,204],"2-elements":[131],"set.":[132],"Note":[133],"$K_{2,2}^{3}$":[135],"well":[138],"known":[139],"generalized":[140],"4-cycle":[141],"$C_4^3$":[142],"(the":[143],"six":[146],"four":[149],"distinct":[150],"edges":[151],"$A,":[152],"B,":[153],"C,":[154],"D$":[155,160],"$A\\cup":[157],"B=":[158],"C\\cup":[159],"$A\\cap":[162],"B=C\\cap":[163],"D=\\emptyset$).":[164],"The":[165],"result":[166],"confirms":[167],"Mycroft's":[168],"conjecture":[169],"$K_{m,m}^{3}$.":[171],"Moreover,":[172],"improve":[174],"term":[177,182,190],"to":[179],"sub-linear":[181,189],"when":[183],"$F=K^3(m)$":[184],"show":[186],"tight":[192],"$K^3(2)$,":[194],"$K^3(m)$":[196],"$3$-partite":[200],"$3$-graph":[201],"size":[206],"$m$.":[207]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}