{"id":"https://openalex.org/W4404822229","doi":"https://doi.org/10.37236/12853","title":"A Note on Graphs of $k$-Colourings","display_name":"A Note on Graphs of $k$-Colourings","publication_year":2024,"publication_date":"2024-11-28","ids":{"openalex":"https://openalex.org/W4404822229","doi":"https://doi.org/10.37236/12853"},"language":"en","primary_location":{"id":"doi:10.37236/12853","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12853","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p48/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085019654","display_name":"Emma Hogan","orcid":null},"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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Emma Hogan","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045091550","display_name":"Alex Scott","orcid":"https://orcid.org/0000-0003-4489-5988"},"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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Scott","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081966233","display_name":"Youri Tamitegama","orcid":"https://orcid.org/0000-0002-8890-683X"},"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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Youri Tamitegama","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018230096","display_name":"Jane Tan","orcid":"https://orcid.org/0000-0003-0536-0374"},"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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jane Tan","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.5764,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71565591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"31","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9746000170707703,"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":0.9746000170707703,"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/T11797","display_name":"graph theory and CDMA systems","score":0.95169997215271,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9164000153541565,"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":0.6302680969238281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4682399332523346}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6302680969238281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4682399332523346}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/12853","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12853","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:0b51e50c-7a5d-4c24-9496-089444c1a607","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"http://purl.org/coar/resource_type/c_dcae04bc"}],"best_oa_location":{"id":"doi:10.37236/12853","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12853","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1940970491","display_name":null,"funder_award_id":"EP/X013642/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G230183981","display_name":"DTP 2224 University of Oxford","funder_award_id":"EP/W524311/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3448263929","display_name":"DMS-EPSRC INDUCED SUBGRAPHS AND GRAPH STRUCTURE","funder_award_id":"EP/X013642/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8235098067","display_name":null,"funder_award_id":"EP/X013642/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404822229.pdf","grobid_xml":"https://content.openalex.org/works/W4404822229.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"For":[0],"a":[1,24],"graph":[2,6,28,56],"$G$,":[3,57,92],"the":[4,30],"$k$-colouring":[5,69],"of":[7,15,74,87,98],"$G$":[8,16,63],"has":[9,38],"vertices":[10],"corresponding":[11],"to":[12],"proper":[13],"$k$-colourings":[14],"and":[17,37,45,78],"edges":[18],"between":[19],"colourings":[20],"that":[21,53,62,83],"differ":[22],"at":[23],"single":[25],"vertex.":[26],"The":[27],"supports":[29],"Glauber":[31],"dynamics":[32],"Markov":[33],"chain":[34],"for":[35,54,91],"$k$-colourings,":[36],"been":[39],"extensively":[40],"studied":[41],"from":[42],"both":[43],"extremal":[44],"probabilistic":[46],"perspectives.":[47],"In":[48],"this":[49],"note,":[50],"we":[51],"show":[52,82],"every":[55],"there":[58],"exists":[59],"$k$":[60],"such":[61],"is":[64],"uniquely":[65,102],"determined":[66],"by":[67],"its":[68,99],"graph,":[70],"confirming":[71],"two":[72],"conjectures":[73],"Asgarli,":[75],"Krehbiel,":[76],"Levinson":[77],"Russell.":[79],"We":[80],"further":[81],"no":[84],"finite":[85],"family":[86],"generalised":[88],"chromatic":[89],"polynomials":[90],"which":[93],"encode":[94],"induced":[95],"subgraph":[96],"counts":[97],"colouring":[100],"graphs,":[101],"determine":[103],"$G$.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
