{"id":"https://openalex.org/W3186330835","doi":"https://doi.org/10.1137/21m1437573","title":"The $\\chi$-Ramsey Problem for Triangle-Free Graphs","display_name":"The $\\chi$-Ramsey Problem for Triangle-Free Graphs","publication_year":2022,"publication_date":"2022-04-28","ids":{"openalex":"https://openalex.org/W3186330835","doi":"https://doi.org/10.1137/21m1437573","mag":"3186330835"},"language":"en","primary_location":{"id":"doi:10.1137/21m1437573","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1437573","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2107.12288","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020874001","display_name":"Ewan Davies","orcid":"https://orcid.org/0000-0002-2699-0976"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"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"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Ewan Davies","raw_affiliation_strings":["Department of Computer Science, University of Colorado Boulder, USA","Mathematical Institute, University of Oxford, UK","DPMMS, University of Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"DPMMS, University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080412993","display_name":"Freddie Illingworth","orcid":"https://orcid.org/0000-0001-5350-2379"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Freddie Illingworth","raw_affiliation_strings":["DPMMS, University of Cambridge, UK","Department of Computer Science, University of Colorado Boulder, USA","Mathematical Institute, University of Oxford, UK"],"affiliations":[{"raw_affiliation_string":"DPMMS, University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Computer Science, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080412993"],"corresponding_institution_ids":["https://openalex.org/I188538660","https://openalex.org/I241749","https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.4509,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63053413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"36","issue":"2","first_page":"1124","last_page":"1134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980000257492065,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9977999925613403,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9961000084877014,"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":0.9085735082626343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8409079313278198},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7165302038192749},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7058408260345459},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.610430121421814},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.579382061958313},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4887978732585907},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4560520648956299},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.42846062779426575},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.41463032364845276},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4059619903564453},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3993174433708191}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9085735082626343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8409079313278198},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7165302038192749},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7058408260345459},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.610430121421814},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.579382061958313},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4887978732585907},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4560520648956299},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.42846062779426575},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.41463032364845276},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4059619903564453},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3993174433708191},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1437573","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1437573","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"},{"id":"pmh:oai:arXiv.org:2107.12288","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.12288","pdf_url":"https://arxiv.org/pdf/2107.12288","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2107.12288","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.12288","pdf_url":"https://arxiv.org/pdf/2107.12288","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":31,"referenced_works":["https://openalex.org/W345637930","https://openalex.org/W1964543450","https://openalex.org/W1984056878","https://openalex.org/W2007851259","https://openalex.org/W2033096960","https://openalex.org/W2063135663","https://openalex.org/W2068871408","https://openalex.org/W2070996481","https://openalex.org/W2074920973","https://openalex.org/W2075303922","https://openalex.org/W2100437838","https://openalex.org/W2106456894","https://openalex.org/W2124046163","https://openalex.org/W2258783555","https://openalex.org/W2747439166","https://openalex.org/W2791579450","https://openalex.org/W2902485876","https://openalex.org/W2903052542","https://openalex.org/W2963927233","https://openalex.org/W3010068861","https://openalex.org/W3014235966","https://openalex.org/W3029889037","https://openalex.org/W3036498058","https://openalex.org/W3043459626","https://openalex.org/W3082695433","https://openalex.org/W3086542228","https://openalex.org/W3099475586","https://openalex.org/W3101393766","https://openalex.org/W3135050051","https://openalex.org/W4212798546","https://openalex.org/W4250476093"],"related_works":["https://openalex.org/W13791998","https://openalex.org/W2474561564","https://openalex.org/W2949231378","https://openalex.org/W4301914467","https://openalex.org/W2127133075","https://openalex.org/W2950410478","https://openalex.org/W4301765976","https://openalex.org/W4297817664","https://openalex.org/W2292548913","https://openalex.org/W2945124636"],"abstract_inverted_index":{"In":[0],"1967,":[1],"Erd\u00f6s":[2,18],"asked":[3],"for":[4,27],"the":[5,28,62,79],"greatest":[6],"chromatic":[7,64],"number,":[8],"$f(n)$,":[9],"amongst":[10],"all":[11],"$n$-vertex,":[12],"triangle-free":[13],"graphs.":[14],"An":[15],"observation":[16],"of":[17,78,81,94],"and":[19,88],"Hajnal":[20],"together":[21],"with":[22],"Shearer's":[23],"classical":[24],"upper":[25],"bound":[26,49,60,75],"off-diagonal":[29],"Ramsey":[30],"number":[31,65,80],"$R(3,":[32],"t)$":[33],"shows":[34],"that":[35,83],"$f(n)$":[36],"is":[37,67,84],"at":[38],"most":[39],"$(2":[40],"\\sqrt{2}":[41],"+":[42],"o(1))":[43],"\\sqrt{n/\\log":[44],"n}$.":[45],"We":[46],"improve":[47],"this":[48],"by":[50],"a":[51,71,92],"factor":[52],"$\\sqrt{2}$,":[53],"as":[54,56],"well":[55],"obtaining":[57],"an":[58],"analogous":[59],"on":[61],"list":[63],"which":[66],"tight":[68,86],"up":[69],"to":[70],"constant":[72],"factor.":[73],"A":[74],"in":[76],"terms":[77],"edges":[82],"similarly":[85],"follows,":[87],"these":[89],"results":[90],"confirm":[91],"conjecture":[93],"Cames":[95],"van":[96],"Batenburg":[97],"et":[98],"al.":[99],"[Electron.":[100],"J.":[101],"Combin.,":[102],"27":[103],"(2020),":[104],"P2.34].":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
