{"id":"https://openalex.org/W2075196560","doi":"https://doi.org/10.1002/rsa.3240060405","title":"On an anti\u2010Ramsey property of Ramanujan graphs","display_name":"On an anti\u2010Ramsey property of Ramanujan graphs","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2075196560","doi":"https://doi.org/10.1002/rsa.3240060405","mag":"2075196560"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240060405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060405","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures & Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060405","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073055503","display_name":"Penny Haxell","orcid":null},"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":false,"raw_author_name":"P. E. Haxell","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom","Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom#TAB#","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025621521","display_name":"Yoshiharu Kohayakawa","orcid":"https://orcid.org/0000-0001-7841-157X"},"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":false,"raw_author_name":"Y. Kohayakawa","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom","Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, United Kingdom#TAB#","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":1.5175,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"6","issue":"4","first_page":"417","last_page":"431"},"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/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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/T10849","display_name":"Finite Group Theory Research","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9002179503440857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7625309824943542},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.6599147319793701},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.542121946811676},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.4890907406806946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38433340191841125}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9002179503440857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7625309824943542},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6599147319793701},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.542121946811676},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.4890907406806946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38433340191841125}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/rsa.3240060405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060405","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures & Algorithms","raw_type":"journal-article"},{"id":"pmh:002946741","is_oa":true,"landing_page_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060405","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.121.3041","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.121.3041","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ime.usp.br/~yoshi/MSs/RoTu/rotu_final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.132.8802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.8802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ime.usp.br/~yoshi/MSs/RoTu/rotu_final.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"pmh:002946741","is_oa":true,"landing_page_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060405","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W82605408","https://openalex.org/W1631603072","https://openalex.org/W1983077071","https://openalex.org/W1993111701","https://openalex.org/W1998400388","https://openalex.org/W2023163209","https://openalex.org/W2057840185","https://openalex.org/W2066486518","https://openalex.org/W2068871408","https://openalex.org/W2073266670","https://openalex.org/W2083870048","https://openalex.org/W2086253307","https://openalex.org/W2097022377","https://openalex.org/W2108124616","https://openalex.org/W2123293563","https://openalex.org/W2137989215","https://openalex.org/W3039948875","https://openalex.org/W4235946010","https://openalex.org/W4241497605"],"related_works":["https://openalex.org/W1492157759","https://openalex.org/W2655188380","https://openalex.org/W2963000151","https://openalex.org/W2742781961","https://openalex.org/W2066767025","https://openalex.org/W1656421143","https://openalex.org/W2962729062","https://openalex.org/W2886974128","https://openalex.org/W2811294698","https://openalex.org/W2144885513"],"abstract_inverted_index":{"Abstract":[0],"If":[1],"G":[2,9,13,24,31,33,82,84,89,94,101,136,138,147,163,172,175,177,183,194,217,219,233,248,258,278,291,296],"and":[3,99,108,209,223,268],"H":[4,11,36,43],"are":[5,212,276],"graphs,":[6,228],"we":[7,199],"write":[8,57],"\u2192":[10,14,102,148,164],"(respectively,":[12,37],"TH":[15],")":[16,44,95,184,195,234,259,292],"if":[17],"for":[18,60,73,127,167,283],"any":[19,74,128],"proper":[20],"edge\u2010coloring":[21],"\u03b3":[22,47],"of":[23,32,42,63,140,215,266,279],"there":[25,78,132,275],"is":[26,48,79,133,271],"a":[27,40,80,122,134],"subgraph":[28],"H'":[29,53],"\u2282":[30],"isomorphic":[34,38],"to":[35,39,161,240,244],"subdivision":[41],"such":[45,86,145,227],"that":[46,87,124,146,201],"injective":[49],"on":[50],"E":[51],"(":[52,93,193,232,247,257,295],").":[54,173,297],"Let":[55],"us":[56],"C":[58,149,165],"l":[59,65,169,231],"the":[61,115,253,264],"cycle":[62],"length":[64],".":[66,105,153],"Spencer":[67],"(cf.":[68],"Erd\u00f6s":[69],"10])":[70],"asked":[71],"whether":[72,274],"g":[75,85,92,98,192,220,246,256,294],"\u2a7e":[76,130],"3":[77,104],"graph":[81,135],"=":[83,137,170,176,181,185,190,218,230,289,293],"(i)":[88,222],"has":[90],"girth":[91,141,282],"at":[96],"least":[97],"(ii)":[100,157],"TC":[103],"Recently,":[106],"R\u00f6dl":[107,267],"Tuza":[109],"[22]":[110],"answered":[111],"this":[112],"question":[113],"in":[114,235,263],"affirmative":[116],"by":[117,206],"proving,":[118],"using":[119],"nonconstructive":[120],"methods,":[121],"result":[123,265],"implies":[125],"that,":[126],"t":[129,139,142,151,178,187],"1,":[131],"+":[143,188],"2":[144,150,186,189,191,255,261],"+2":[152],"In":[154],"particular,":[155],"condition":[156],"may":[158,237],"be":[159,238,241],"strengthened":[160],"(iii)":[162,224,236,285],"\ud835\udcc1":[166,180,229,288],"some":[168],"\ud835\udcc1(":[171,182,290],"For":[174,226],"above":[179],"\u2212":[196,260],"2.":[197],"Here,":[198],"show":[200],"suitable":[202],"Ramanujan":[203],"graphs":[204,216,277],"constructed":[205],"Lubotzky,":[207],"Phillips,":[208],"Sarnak":[210],"[18]":[211],"explicit":[213],"examples":[214],"satisfying":[221],"above.":[225],"taken":[239],"roughly":[242],"equal":[243],"(3/2)":[245],"),":[249],"thus":[250],"considerably":[251],"improving":[252],"value":[254],"given":[262],"Tuza.":[269],"It":[270],"not":[272],"known":[273],"arbitrarily":[280],"large":[281],"which":[284],"holds":[286],"with":[287]},"counts_by_year":[{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}