{"id":"https://openalex.org/W1994526721","doi":"https://doi.org/10.1112/jlms/jdu004","title":"The Ramsey number of the clique and the hypercube","display_name":"The Ramsey number of the clique and the hypercube","publication_year":2014,"publication_date":"2014-03-07","ids":{"openalex":"https://openalex.org/W1994526721","doi":"https://doi.org/10.1112/jlms/jdu004","mag":"1994526721"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu004","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu004","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1306.0461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020452147","display_name":"Gonzalo Fiz Pontiveros","orcid":null},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Gonzalo Fiz Pontiveros","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077696461","display_name":"Simon Griffiths","orcid":"https://orcid.org/0000-0003-2435-7963"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Simon Griffiths","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029881267","display_name":"Robert Morris","orcid":"https://orcid.org/0000-0002-7826-7907"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Robert Morris","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028282339","display_name":"David Saxton","orcid":"https://orcid.org/0000-0003-1043-6150"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"David Saxton","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bota\u0302nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil, gf232@impa.br, sgriff@impa.br, saxton@impa.br","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017513172","display_name":"Jozef Skokan","orcid":"https://orcid.org/0000-0003-3996-7676"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jozef Skokan","raw_affiliation_strings":["Department of Mathematics, LSE, Houghton Street, London, WC2A 2AE, United Kingdom","Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA, j.skokan@lse.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, LSE, Houghton Street, London, WC2A 2AE, United Kingdom","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA, j.skokan@lse.ac.uk","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029881267"],"corresponding_institution_ids":["https://openalex.org/I141883831"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":2.1422,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83939039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"89","issue":"3","first_page":"680","last_page":"702"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9957000017166138,"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":0.9058075547218323},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.8160735368728638},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.749208390712738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6220367550849915},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5719611048698425},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.4930102527141571},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.47487160563468933},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.4564019739627838},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44957244396209717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1538102626800537}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9058075547218323},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.8160735368728638},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.749208390712738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6220367550849915},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5719611048698425},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.4930102527141571},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47487160563468933},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.4564019739627838},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44957244396209717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1538102626800537},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1112/jlms/jdu004","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu004","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lse.ac.uk:57071","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-3996-7676>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1306.0461","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.0461","pdf_url":"https://arxiv.org/pdf/1306.0461","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":[],"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:CiteSeerX.psu:10.1.1.766.4253","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.4253","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1306.0461.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1306.0461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1306.0461","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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1306.0461","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.0461","pdf_url":"https://arxiv.org/pdf/1306.0461","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1444168583","https://openalex.org/W1487872891","https://openalex.org/W1588853369","https://openalex.org/W1606812353","https://openalex.org/W1790340838","https://openalex.org/W1890577096","https://openalex.org/W1964543450","https://openalex.org/W1992843513","https://openalex.org/W2007801688","https://openalex.org/W2030551570","https://openalex.org/W2034622005","https://openalex.org/W2037159051","https://openalex.org/W2037951482","https://openalex.org/W2045472305","https://openalex.org/W2068871408","https://openalex.org/W2069367490","https://openalex.org/W2074920973","https://openalex.org/W2082497622","https://openalex.org/W2095689360","https://openalex.org/W2100437838","https://openalex.org/W2103032535","https://openalex.org/W2137574596","https://openalex.org/W2137669983","https://openalex.org/W2145062394","https://openalex.org/W2155870908","https://openalex.org/W2169821423","https://openalex.org/W2949563517","https://openalex.org/W2950515403","https://openalex.org/W2977322974","https://openalex.org/W3101393766","https://openalex.org/W4241860363","https://openalex.org/W6680388155"],"related_works":["https://openalex.org/W1519742024","https://openalex.org/W1614685472","https://openalex.org/W2084021260","https://openalex.org/W3026920247","https://openalex.org/W2066456778","https://openalex.org/W2982077839","https://openalex.org/W2519130717","https://openalex.org/W2133449501","https://openalex.org/W1968040870","https://openalex.org/W1980196194"],"abstract_inverted_index":{"The":[0],"Ramsey":[1],"number":[2],"r":[3,75],"(":[4,76,84,89],"K":[5,29,77],"s":[6,45,78,85,99],",":[7,79],"Q":[8,80],"n":[9,81,91,106],")":[10,82,88,94],"is":[11],"the":[12,23,26,69],"smallest":[13],"positive":[14],"integer":[15],"N":[16,30,32,101,108],"such":[17],"that":[18,74],"every":[19,98,103],"red\u2013blue":[20],"colouring":[21],"of":[22,25,50,61,68],"edges":[24],"complete":[27],"graph":[28],"on":[31,44,58],"vertices":[33],"contains":[34],"either":[35],"a":[36,41,48],"red":[37],"n-dimensional":[38],"hypercube,":[39],"or":[40],"blue":[42],"clique":[43],"vertices.":[46],"Answering":[47],"question":[49],"Burr":[51],"and":[52,56,65,67,102],"Erd\u0151s":[53],"from":[54],"1983,":[55],"improving":[57],"recent":[59],"results":[60],"Conlon,":[62],"Fox,":[63],"Lee":[64],"Sudakov,":[66],"current":[70],"authors,":[71],"we":[72],"show":[73],"=":[83],"\u2212":[86,92],"1":[87,93,96],"2":[90],"+":[95],"for":[97],"\u2208":[100,107],"sufficiently":[104],"large":[105],".":[109]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}