{"id":"https://openalex.org/W2799411888","doi":"https://doi.org/10.1017/s0963548318000172","title":"A (5,5)-Colouring of <i>K</i><sub><i>n</i></sub> with Few Colours","display_name":"A (5,5)-Colouring of <i>K</i><sub><i>n</i></sub> with Few Colours","publication_year":2018,"publication_date":"2018-05-09","ids":{"openalex":"https://openalex.org/W2799411888","doi":"https://doi.org/10.1017/s0963548318000172","mag":"2799411888"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548318000172","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000172","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102937543","display_name":"Alex Cameron","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"ALEX CAMERON","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA (e-mail:","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102885100","display_name":"Emily Heath","orcid":"https://orcid.org/0000-0001-6034-4241"},"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":"EMILY HEATH","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (e-mail:","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102937543"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.1288,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.45681925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"6","first_page":"892","last_page":"912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.6948999762535095,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.6948999762535095,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8838695287704468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7560178637504578},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5599673986434937},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5555093884468079},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5026669502258301},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37651655077934265}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8838695287704468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7560178637504578},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5599673986434937},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5555093884468079},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5026669502258301},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37651655077934265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548318000172","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000172","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1600793037","https://openalex.org/W1974757655","https://openalex.org/W1994434808","https://openalex.org/W2030215923","https://openalex.org/W2044397349","https://openalex.org/W2062230178","https://openalex.org/W2071449493","https://openalex.org/W2072455759","https://openalex.org/W2072808987","https://openalex.org/W2079576387","https://openalex.org/W2091175510","https://openalex.org/W7064449661"],"related_works":["https://openalex.org/W2385671392","https://openalex.org/W2610737932","https://openalex.org/W4225966317","https://openalex.org/W2358150931","https://openalex.org/W2383129606","https://openalex.org/W2042289434","https://openalex.org/W4318146752","https://openalex.org/W2073908095","https://openalex.org/W4225726351","https://openalex.org/W2952342369"],"abstract_inverted_index":{"For":[0],"fixed":[1],"integers":[2],"p":[3,12,40,58],"and":[4,102,104],"q":[5,14,45,60],",":[6,11,13,59],"let":[7],"f":[8,70],"(":[9,57,71,95],"n":[10,34,72,75,81,96,115],")":[15,98],"denote":[16],"the":[17,27,30,87,109],"minimum":[18],"number":[19],"of":[20,26,29,39,93],"colours":[21],"needed":[22],"to":[23,107],"colour":[24],"all":[25],"edges":[28],"complete":[31],"graph":[32],"K":[33],"such":[35],"that":[36,67,69],"no":[37],"clique":[38],"vertices":[41],"spans":[42],"fewer":[43],"than":[44],"distinct":[46],"colours.":[47],"Any":[48],"edge-colouring":[49],"with":[50],"this":[51],"property":[52],"is":[53],"known":[54,89,111],"as":[55,80],"a":[56],")-colouring.":[61],"We":[62],"construct":[63],"an":[64],"explicit":[65],"(5,5)-colouring":[66],"shows":[68],",5,5)":[73],"\u2264":[74],"1/3":[76,116],"+":[77],"o":[78],"(1)":[79],"\u2192":[82],"\u221e.":[83],"This":[84],"improves":[85],"upon":[86],"best":[88,110],"probabilistic":[90],"upper":[91],"bound":[92,113],"O":[94],"1/2":[97],"given":[99],"by":[100],"Erd\u0151s":[101],"Gy\u00e1rf\u00e1s,":[103],"comes":[105],"close":[106],"matching":[108],"lower":[112],"\u03a9(":[114],").":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
