{"id":"https://openalex.org/W4235676350","doi":"https://doi.org/10.1017/s0963548306007954","title":"Colouring Random Regular Graphs","display_name":"Colouring Random Regular Graphs","publication_year":2006,"publication_date":"2006-09-11","ids":{"openalex":"https://openalex.org/W4235676350","doi":"https://doi.org/10.1017/s0963548306007954"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306007954","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007954","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/A5030575696","display_name":"LINGSHENG SHI","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"LINGSHENG SHI","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail:","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113900323","display_name":"Nicholas Wormald","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"NICHOLAS WORMALD","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030575696"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":2.0668037,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84915663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"3","first_page":"459","last_page":"494"},"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":0.722000002861023,"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":0.722000002861023,"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":0.6886000037193298,"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/mathematics","display_name":"Mathematics","score":0.7817873358726501},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.7138800024986267},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6796292066574097},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6302114129066467},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5649464726448059},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.5109909772872925},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4807015061378479},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.4631155729293823},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4500215947628021},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1859317421913147},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.16432270407676697},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.12068614363670349},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08066779375076294}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817873358726501},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.7138800024986267},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6796292066574097},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6302114129066467},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5649464726448059},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.5109909772872925},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4807015061378479},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.4631155729293823},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4500215947628021},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1859317421913147},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.16432270407676697},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.12068614363670349},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08066779375076294}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548306007954","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007954","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1525926546","https://openalex.org/W1978113428","https://openalex.org/W1979720612","https://openalex.org/W2003791246","https://openalex.org/W2018483383","https://openalex.org/W2022743540","https://openalex.org/W2022956475","https://openalex.org/W2037125727","https://openalex.org/W2054040057","https://openalex.org/W2080547399","https://openalex.org/W2094803507","https://openalex.org/W2139757566","https://openalex.org/W6684173588","https://openalex.org/W6746300640"],"related_works":["https://openalex.org/W2012853908","https://openalex.org/W2092565550","https://openalex.org/W2170524605","https://openalex.org/W4250665764","https://openalex.org/W2963998228","https://openalex.org/W365256087","https://openalex.org/W2497425261","https://openalex.org/W3130470475","https://openalex.org/W2071911310","https://openalex.org/W4235676350"],"abstract_inverted_index":{"In":[0],"a":[1,7,27,45,62],"previous":[2],"paper":[3],"we":[4,20],"showed":[5],"that":[6,26,40],"random":[8,28,46,98],"4-regular":[9],"graph":[10,30,49],"asymptotically":[11,31],"almost":[12,32],"surely":[13,33],"(a.a.s.)":[14,34],"has":[15,35],"chromatic":[16,36,42],"number":[17,37,43,102],"3.":[18],"Here":[19],"extend":[21],"the":[22,41,101,107,115],"method":[23],"to":[24,61],"show":[25],"6-regular":[29],"4":[38],"and":[39,55,82],"of":[44,64,103,122,125],"d":[47,52,71,77,86],"-regular":[48],"for":[50,70,76,85],"other":[51],"between":[53],"5":[54],"10":[56],"inclusive":[57],"is":[58],"a.a.s.":[59,95],"restricted":[60],"range":[63],"two":[65],"integer":[66],"values:":[67],"{3,":[68],"4}":[69],"=":[72,78,87],"5,":[73],"{4,":[74],"5}":[75],"7,":[79],"8,":[80],"9,":[81],"{5,":[83],"6}":[84],"10.":[88],"The":[89],"proof":[90],"uses":[91],"efficient":[92],"algorithms":[93,111],"which":[94],"colour":[96],"these":[97],"graphs":[99],"using":[100,114],"colours":[104],"specified":[105],"by":[106],"upper":[108],"bound.":[109],"These":[110],"are":[112],"analysed":[113],"differential":[116,126],"equation":[117],"method,":[118],"including":[119],"an":[120],"analysis":[121],"certain":[123],"systems":[124],"equations":[127],"with":[128],"discontinuous":[129],"right-hand":[130],"sides.":[131]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}