{"id":"https://openalex.org/W2996267286","doi":"https://doi.org/10.37236/9223","title":"Graphs with no Induced $K_{2, t}$","display_name":"Graphs with no Induced $K_{2, t}$","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W2996267286","doi":"https://doi.org/10.37236/9223","mag":"2996267286"},"language":"en","primary_location":{"id":"doi:10.37236/9223","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9223","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p19/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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p19/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080412993","display_name":"Freddie Illingworth","orcid":"https://orcid.org/0000-0001-5350-2379"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Freddie Illingworth","raw_affiliation_strings":["University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080412993"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":1.8556,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80051813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"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":0.44366705417633057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3731597065925598}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44366705417633057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3731597065925598}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9223","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9223","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p19/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"},{"id":"pmh:oai:arXiv.org:1912.07970","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.07970","pdf_url":"https://arxiv.org/pdf/1912.07970","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,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10189640","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10189640/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics , 28 (1) , Article P1.19. (2021)","raw_type":"Article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:a515cef0-3cd7-4b45-9fd2-b1bd177bffc3","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.37236/9223","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9223","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p19/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":[{"id":"https://openalex.org/G4187749247","display_name":null,"funder_award_id":"2114463","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2996267286.pdf","grobid_xml":"https://content.openalex.org/works/W2996267286.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1487872891","https://openalex.org/W1964543450","https://openalex.org/W1966724030","https://openalex.org/W2066118197","https://openalex.org/W2069367490","https://openalex.org/W2080305978","https://openalex.org/W2111007781","https://openalex.org/W2532317049","https://openalex.org/W2905110430","https://openalex.org/W2919892317","https://openalex.org/W3009933977","https://openalex.org/W3104234972"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Consider":[0],"a":[1,33,94,97],"graph":[2],"$G$":[3,30],"on":[4],"$n$":[5],"vertices":[6],"with":[7],"$\\alpha":[8,55,61],"\\binom{n}{2}$":[9],"edges":[10],"which":[11,72],"does":[12],"not":[13],"contain":[14],"an":[15],"induced":[16],"$K_{2,":[17],"t}$":[18],"($t":[19],"\\geqslant":[20],"2$).":[21],"How":[22],"large":[23,34],"must":[24],"$\\alpha$":[25,48,83],"be":[26,91],"to":[27,67],"ensure":[28],"that":[29],"contains,":[31],"say,":[32],"clique":[35],"or":[36],"some":[37],"fixed":[38],"subgraph":[39],"$H$?":[40],"We":[41],"give":[42],"results":[43,59,89],"for":[44,47,54,60],"two":[45],"regimes:":[46],"bounded":[49,84],"away":[50,85],"from":[51,86],"zero":[52],"and":[53,80,102,104],"=":[56,62],"o(1)$.":[57],"Our":[58],"o(1)$":[63],"are":[64],"strongly":[65],"related":[66],"the":[68],"Induced":[69],"Tur\u00e1n":[70],"numbers":[71],"were":[73],"recently":[74,106],"introduced":[75],"by":[76],"Loh,":[77],"Tait,":[78],"Timmons":[79],"Zhou.":[81],"For":[82],"zero,":[87],"our":[88],"can":[90],"seen":[92],"as":[93],"generalisation":[95],"of":[96,99],"result":[98],"Gy\u00e1rf\u00e1s,":[100],"Hubenko":[101],"Solymosi":[103],"more":[105],"Holmsen":[107],"(whose":[108],"argument":[109],"inspired":[110],"ours).":[111]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}