{"id":"https://openalex.org/W3093711160","doi":"https://doi.org/10.1017/s0963548320000139","title":"Frozen (\u0394 + 1)-colourings of bounded degree graphs","display_name":"Frozen (\u0394 + 1)-colourings of bounded degree graphs","publication_year":2020,"publication_date":"2020-10-19","ids":{"openalex":"https://openalex.org/W3093711160","doi":"https://doi.org/10.1017/s0963548320000139","mag":"3093711160"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548320000139","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548320000139","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2117/345627","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029166445","display_name":"Marthe Bonamy","orcid":"https://orcid.org/0000-0001-7905-8018"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marthe Bonamy","raw_affiliation_strings":["CNRS, LaBRI, Universit\u00e9 de Bordeaux, France"],"affiliations":[{"raw_affiliation_string":"CNRS, LaBRI, Universit\u00e9 de Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210160189","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044190443","display_name":"Nicol\u00e1s Bousquet","orcid":"https://orcid.org/0000-0003-0170-0503"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210155607","display_name":"Laboratoire d'Informatique en Images et Syst\u00e8mes d'Information","ror":"https://ror.org/04dv4he91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I188626449","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210155607","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Bousquet","raw_affiliation_strings":["LIRIS, CNRS, Universit\u00e9 Claude Bernard Lyon 1, Lyon, France"],"affiliations":[{"raw_affiliation_string":"LIRIS, CNRS, Universit\u00e9 Claude Bernard Lyon 1, Lyon, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210155607","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086363230","display_name":"Guillem Perarnau","orcid":"https://orcid.org/0000-0002-1953-9511"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Guillem Perarnau","raw_affiliation_strings":["Departament de Matem\u00e0tiques (MAT), Universitat Polit\u00e8cnica de Catalunya (UPC), Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques (MAT), Universitat Polit\u00e8cnica de Catalunya (UPC), Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086363230"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":0.6613,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72743785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"30","issue":"3","first_page":"330","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.995199978351593,"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":0.8849270343780518},{"id":"https://openalex.org/keywords/glauber","display_name":"Glauber","score":0.7956204414367676},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6480320692062378},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.529583215713501},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4976983368396759},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48519352078437805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42545977234840393},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17909520864486694}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8849270343780518},{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.7956204414367676},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6480320692062378},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.529583215713501},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4976983368396759},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48519352078437805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42545977234840393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17909520864486694},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548320000139","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548320000139","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"},{"id":"pmh:oai:HAL:hal-03829750v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03829750","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2021, 30 (3), pp.330-343. &#x27E8;10.1017/S0963548320000139&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:upcommons.upc.edu:2117/345627","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/345627","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/345627","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/345627","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1588967885","https://openalex.org/W1873885073","https://openalex.org/W1917899534","https://openalex.org/W1976090101","https://openalex.org/W1976445742","https://openalex.org/W1979487401","https://openalex.org/W1997048861","https://openalex.org/W2012032973","https://openalex.org/W2014487253","https://openalex.org/W2109260999","https://openalex.org/W2279676320","https://openalex.org/W2798588639","https://openalex.org/W2898624802","https://openalex.org/W2950027515","https://openalex.org/W2963305098","https://openalex.org/W2963510032","https://openalex.org/W2964080237","https://openalex.org/W3098791681","https://openalex.org/W3102118427","https://openalex.org/W3111890340"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1515414572","https://openalex.org/W2950956395","https://openalex.org/W2560371573","https://openalex.org/W2173245850","https://openalex.org/W2079317597","https://openalex.org/W2025229065","https://openalex.org/W2045631952","https://openalex.org/W2031523256","https://openalex.org/W2089700575"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"G":[2,24,34,127,136],"be":[3,17,204],"a":[4,85,165],"graph":[5,22,27,57,81],"on":[6],"n":[7,141,177,179,206],"vertices":[8,29,108],"and":[9,14,35,66,94,222,225],"with":[10,219],"maximum":[11],"degree":[12],"\u0394,":[13],"let":[15],"k":[16,31,38,55],"an":[18],"integer.":[19],"The":[20],"k-recolouring":[21],"of":[23,33,89,106,132,135,146,152,160,164,174,191,217],"is":[25,50,58,82,122,128,137],"the":[26,54,77,104,114,130,143,150,153,158,170,188,192,215],"whose":[28],"are":[30,40],"-colourings":[32,39],"where":[36],"two":[37],"adjacent":[41],"if":[42,126],"they":[43],"differ":[44],"at":[45,91],"exactly":[46],"one":[47],"vertex.":[48],"It":[49],"well":[51],"known":[52],"that":[53,76,125,187],"-recolouring":[56],"connected":[59,87],"for":[60,181,195],"$k\\geq":[61,182],"\\Delta+2$":[62,183],".":[63],"Feghali,":[64],"Johnson":[65],"Paulusma":[67],"(":[68,176],"J.":[69],"Graph":[70],"Theory":[71],"83":[72],"(2016)":[73],"340\u2013358)":[74],"showed":[75],"(\u0394":[78,115,161,196],"+":[79,116,162,197],"1)-recolouring":[80,117],"composed":[83],"by":[84],"unique":[86],"component":[88],"size":[90],"least":[92],"2":[93,207],"(possibly":[95],"many)":[96],"isolated":[97,107],"vertices.":[98],"In":[99,167],"this":[100],"paper,":[101],"we":[102,185,210],"study":[103,226],"proportion":[105,131],"(also":[109],"called":[110],"frozen":[111,133,223,227],"colourings)":[112],"in":[113,140,229],"graph.":[118,166],"Our":[119],"first":[120],"contribution":[121],"to":[123,156,169,200],"show":[124,186],"connected,":[129],"colourings":[134,202,228],"exponentially":[138],"smaller":[139],"than":[142],"total":[144],"number":[145,159],"colourings.":[147],"This":[148],"motivates":[149],"use":[151],"Glauber":[154,193],"dynamics":[155,194],"approximate":[157],"1)-colourings":[163,198],"contrast":[168],"conjectured":[171],"mixing":[172,189],"time":[173,190],"O":[175],"log":[178],")":[180],"colours,":[184],"restricted":[199],"non-frozen":[201],"can":[203],"\u03a9(":[205],").":[208],"Finally,":[209],"prove":[211],"some":[212],"results":[213],"about":[214],"existence":[216],"graphs":[218],"large":[220],"girth":[221],"colourings,":[224],"random":[230],"regular":[231],"graphs.":[232]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-10-29T00:00:00"}
