{"id":"https://openalex.org/W3010398943","doi":"https://doi.org/10.1137/19m1265442","title":"Tur\u00e1n Numbers of Bipartite Subdivisions","display_name":"Tur\u00e1n Numbers of Bipartite Subdivisions","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3010398943","doi":"https://doi.org/10.1137/19m1265442","mag":"3010398943"},"language":"en","primary_location":{"id":"doi:10.1137/19m1265442","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1265442","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101911266","display_name":"Tao Jiang","orcid":"https://orcid.org/0000-0003-3833-4498"},"institutions":[{"id":"https://openalex.org/I83328450","display_name":"Miami University","ror":"https://ror.org/05nbqxr67","country_code":"US","type":"education","lineage":["https://openalex.org/I83328450"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tao Jiang","raw_affiliation_strings":["Department of Mathematics, Miami University, Oxford, OH 45056, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Miami University, Oxford, OH 45056, USA","institution_ids":["https://openalex.org/I83328450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009439657","display_name":"Yu Qiu","orcid":"https://orcid.org/0000-0002-2078-0513"},"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":"Yu Qiu","raw_affiliation_strings":["School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P.R. China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101911266"],"corresponding_institution_ids":["https://openalex.org/I83328450"],"apc_list":null,"apc_paid":null,"fwci":4.3809,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.95135468,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"34","issue":"1","first_page":"556","last_page":"570"},"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":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9951000213623047,"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/T11476","display_name":"Graph theory and applications","score":0.9884999990463257,"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":0.8462660312652588},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7947244644165039},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7692133188247681},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7627125978469849},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.6220840811729431},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.557772159576416},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47978025674819946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41758644580841064}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8462660312652588},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7947244644165039},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7692133188247681},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7627125978469849},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.6220840811729431},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.557772159576416},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47978025674819946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41758644580841064}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1265442","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1265442","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8253768588","display_name":null,"funder_award_id":"DMS-1855542","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8589651859","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1444168583","https://openalex.org/W1966571632","https://openalex.org/W1983946246","https://openalex.org/W1995481390","https://openalex.org/W1996268095","https://openalex.org/W2009852526","https://openalex.org/W2035971565","https://openalex.org/W2080305978","https://openalex.org/W2111007781","https://openalex.org/W2148275926","https://openalex.org/W2155085924","https://openalex.org/W2169821423","https://openalex.org/W3100868007"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W2036057584","https://openalex.org/W245205139","https://openalex.org/W2921162226","https://openalex.org/W4234658180","https://openalex.org/W2107875203","https://openalex.org/W4235849992","https://openalex.org/W4246000090","https://openalex.org/W3143578817","https://openalex.org/W2910933086"],"abstract_inverted_index":{"Given":[0],"a":[1,25,56,92,113,187,251],"graph":[2,17,76,82,189],"$H$,":[3],"the":[4,9,35,43,75,79,103,150,157,196,219,239,246,255],"Tur\u00e1n":[5,44,178,206,221],"number":[6,11],"$\\mathrm{ex}(n,H)$":[7],"is":[8],"largest":[10],"of":[12,28,38,46,58,94,116,153,160,208,238,254],"edges":[13],"in":[14,50,89],"an":[15,236],"$H$-free":[16],"on":[18,24,34,42,55,235],"$n$":[19],"vertices.":[20],"We":[21,242],"make":[22],"progress":[23,54],"recent":[26],"conjecture":[27,57,166,257],"Conlon,":[29,131,228],"Janzer,":[30,132,229],"and":[31,60,99,118,133,203,216,226,230],"Lee":[32,134],"[More":[33],"Extremal":[36],"Number":[37],"Subdivisions,":[39],"arXiv:1903.10631v1,":[40],"2019]":[41],"numbers":[45],"bipartite":[47,81,188],"graphs,":[48],"which":[49,184],"turn":[51],"yields":[52],"further":[53],"Erd\u00f6s":[59],"Simonovits":[61],"[Combinatorica,":[62],"1":[63],"(1981),":[64],"pp.":[65,127],"25--42].":[66],"Let":[67,72],"$s,t,k\\geq":[68,141],"2$":[69],"be":[70],"integers.":[71],"$K_{s,t}^k$":[73],"denote":[74],"obtained":[77,199],"from":[78,112],"complete":[80],"$K_{s,t}$":[83],"by":[84,200,213,227],"replacing":[85,105],"each":[86],"edge":[87],"$uv$":[88],"it":[90],"with":[91,191],"path":[93],"length":[95],"$k$":[96],"between":[97],"$u$":[98],"$v$":[100],"such":[101],"that":[102,129,137,245],"$st$":[104],"paths":[106],"are":[107],"internally":[108],"disjoint.":[109],"It":[110],"follows":[111],"general":[114],"theorem":[115],"Bukh":[117],"Conlon":[119],"[J.":[120],"Eur.":[121],"Math.":[122],"Soc.":[123],"(JEMS),":[124],"20":[125],"(2018),":[126],"1747--1757]":[128],"$\\mathrm{ex}(n,K_{s,t}^k)=\\Omega(n^{1+\\frac{1}{k}-\\frac{1}{sk}})$.":[130],"recently":[135,198],"conjectured":[136],"for":[138,167,183,258],"any":[139],"integers":[140],"2$,":[142],"$\\mathrm{ex}(n,K_{s,t}^k)=O(n^{1+\\frac{1}{k}-\\frac{1}{sk}})$.":[143],"Among":[144],"many":[145,175],"other":[146],"things,":[147],"they":[148],"settled":[149],"$k=2$":[151],"case":[152],"their":[154,165],"conjecture.":[155],"As":[156],"main":[158,170],"result":[159],"this":[161],"paper,":[162],"we":[163],"prove":[164],"$k=3,4$.":[168],"Our":[169,232],"results":[171],"also":[172,243,249],"yield":[173],"infinitely":[174],"new":[176],"so-called":[177],"exponents:":[179],"rationals":[180],"$r\\in":[181],"(1,2)$":[182],"there":[185],"exists":[186],"$H$":[190],"$\\mathrm{ex}(n,":[192],"H)=\\Theta(n^r)$,":[193],"adding":[194],"to":[195],"lists":[197],"Jiang,":[201],"Ma,":[202],"Yepremyan":[204],"[On":[205,218],"Exponents":[207],"Bipartite":[209],"Graphs,":[210],"arXiv:1806.02838,":[211],"2018],":[212,225],"Kang,":[214],"Kim,":[215],"Liu":[217],"Rational":[220],"Exponent":[222],"Conjecture,":[223],"arXiv:1811.06916,":[224],"Lee.":[231],"method":[233,248],"builds":[234],"extension":[237],"Conlon--Janzer--Lee":[240,256],"method.":[241],"note":[244],"extended":[247],"gives":[250],"weaker":[252],"version":[253],"all":[259],"$k\\geq":[260],"2$.":[261]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}