{"id":"https://openalex.org/W1835305721","doi":"https://doi.org/10.37236/2471","title":"An Ordered Tur\u00e1n Problem for Bipartite Graphs","display_name":"An Ordered Tur\u00e1n Problem for Bipartite Graphs","publication_year":2012,"publication_date":"2012-12-13","ids":{"openalex":"https://openalex.org/W1835305721","doi":"https://doi.org/10.37236/2471","mag":"1835305721"},"language":"en","primary_location":{"id":"doi:10.37236/2471","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2471","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p43/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":null,"license_id":null,"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/v19i4p43/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056721527","display_name":"Craig Timmons","orcid":"https://orcid.org/0000-0001-8591-4773"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Craig Timmons","raw_affiliation_strings":["University of California San Diego","University of California,  San Diego"],"affiliations":[{"raw_affiliation_string":"University of California San Diego","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California,  San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056721527"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05242776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"4","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":0.9998000264167786,"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":0.9998000264167786,"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":0.982699990272522,"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":0.9718999862670898,"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/combinatorics","display_name":"Combinatorics","score":0.9045700430870056},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8302862048149109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.746536910533905},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5508756637573242},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5304597616195679},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4957159757614136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36223104596138}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9045700430870056},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8302862048149109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.746536910533905},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5508756637573242},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5304597616195679},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4957159757614136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36223104596138}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2471","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2471","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p43/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":null,"license_id":null,"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:10.37236/2471","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2471","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p43/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":null,"license_id":null,"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/W1835305721.pdf","grobid_xml":"https://content.openalex.org/works/W1835305721.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W104057383","https://openalex.org/W181128013","https://openalex.org/W1444168583","https://openalex.org/W1510730180","https://openalex.org/W1520001339","https://openalex.org/W1569752386","https://openalex.org/W1663749032","https://openalex.org/W1968319543","https://openalex.org/W1977374427","https://openalex.org/W1987996179","https://openalex.org/W1992473680","https://openalex.org/W2002448734","https://openalex.org/W2004073925","https://openalex.org/W2006135590","https://openalex.org/W2009852526","https://openalex.org/W2009888012","https://openalex.org/W2016480989","https://openalex.org/W2019898392","https://openalex.org/W2028340927","https://openalex.org/W2050102435","https://openalex.org/W2052325621","https://openalex.org/W2080305978","https://openalex.org/W2093219044","https://openalex.org/W2110805362","https://openalex.org/W2148275926","https://openalex.org/W2289451060","https://openalex.org/W4298414065","https://openalex.org/W6602945294","https://openalex.org/W6628667382","https://openalex.org/W6655579563"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W245205139","https://openalex.org/W2036057584","https://openalex.org/W4246000090","https://openalex.org/W2516280752","https://openalex.org/W2107875203","https://openalex.org/W4234658180","https://openalex.org/W4235849992","https://openalex.org/W2910933086","https://openalex.org/W3143578817"],"abstract_inverted_index":{"Let":[0,69],"$F$":[1,15],"be":[2,71],"a":[3,17,48,72,102,189],"graph.":[4],"A":[5,96,136],"graph":[6,35,73,105,192],"$G$":[7,70,88],"is":[8,26,47,101,139],"$F$-free":[9,34],"if":[10],"it":[11],"does":[12],"not":[13],"contain":[14],"as":[16,89],"subgraph.":[18],"The":[19,39],"Tur\u00e1n":[20,42,64,168],"number":[21,29],"of":[22,30,41,44,62,87,151,162],"$F$,":[23],"written":[24],"$\\textrm{ex}(n,F)$,":[25],"the":[27,63,85,93,131,154,160,167],"maximum":[28],"edges":[31],"in":[32,92,146,153],"an":[33,59,140],"with":[36,74,193],"$n$":[37,186],"vertices.":[38],"determination":[40],"numbers":[43,169],"bipartite":[45,67,104],"graphs":[46],"challenging":[49],"and":[50,83,119,171],"widely":[51],"investigated":[52],"problem.":[53],"In":[54,173],"this":[55],"paper":[56],"we":[57,175,187],"introduce":[58],"ordered":[60,91],"version":[61],"problem":[65],"for":[66,159],"graphs.":[68],"$V(G)":[75],"=":[76,110,121],"\\{1,":[77],"2,":[78],"\\dots":[79,115,126],",":[80],"n":[81],"\\}$":[82,118,129],"view":[84],"vertices":[86,145],"being":[90],"natural":[94],"way.":[95],"zig-zag":[97,137,163],"$K_{s,t}$,":[98],"denoted":[99],"$Z_{s,t}$,":[100],"complete":[103],"$K_{s,t}$":[106],"whose":[107,144],"parts":[108],"$A":[109],"\\{n_1":[111],"&lt;":[112,114,116,123,125,127,134],"n_2":[113],"n_s":[117],"$B":[120],"\\{m_1":[122],"m_2":[124],"m_t":[128],"satisfy":[130],"condition":[132],"$n_s":[133],"m_1$.":[135],"$C_{2k}$":[138,143],"even":[141],"cycle":[142],"one":[147],"part":[148],"precede":[149],"all":[150],"those":[152],"other":[155],"part.":[156],"Write":[157],"$\\mathcal{Z}_{2k}$":[158],"family":[161],"$2k$-cycles.":[164],"We":[165],"investigate":[166],"$\\textrm{ex}(n,Z_{s,t})$":[170],"$\\textrm{ex}(n,\\mathcal{Z}_{2k})$.":[172],"particular":[174],"show":[176],"$\\textrm{ex}(n,":[177],"Z_{2,2})":[178],"\\leq":[179],"\\frac{2}{3}n^{3/2}":[180],"+":[181,201],"O(n^{5/4})$.":[182],"For":[183],"infinitely":[184],"many":[185],"construct":[188],"$Z_{2,2}$-free":[190],"$n$-vertex":[191],"more":[194],"than":[195],"$(n":[196],"-":[197,199],"\\sqrt{n}":[198],"1)":[200],"\\textrm{ex}":[202],"(n,K_{2,2})$":[203],"edges.":[204]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
